Exponents and Powers Class 8 Extra Questions and Answers Free PDF Download
Very Short Answer Questions 1 Marks
1. \[\mathrm{3}\] multiplied fifteen times is written as?
Ans:
\[3\] Multiplied for fifteen times is written as
\[3\times 3\times 3\times 3\times 3\ldots 15 times={{3}^{15}}\]
Answer will be \[{{3}^{15}}\]
2. What is the base of the exponent \[{{\mathrm{6}}^{\mathrm{9}}}\]?
\[\begin{align} & \mathrm{(a)6} \\ & \mathrm{(b)2} \\ & \mathrm{(c)9} \\ & \mathrm{(d)None} \\ \end{align}\]
Ans:
The base of the exponent \[{{6}^{9}}\] is \[6\]
3. Find the missing number \[{{\mathrm{7}}^{\mathrm{5}}}\mathrm{=}\dfrac{\mathrm{1}}{{{\mathrm{7}}^{\square }}}\]?
\[\begin{align} & \mathrm{(a)2} \\ & \mathrm{(b)-5} \\ & \mathrm{(c)1} \\ & \mathrm{(d)None} \\ \end{align}\]
Ans:
The missing number should be \[-5\]
So the answer will be \[{{7}^{5}}=\dfrac{1}{{{7}^{-5}}}\]
4. Find the value of \[{{\left( {{\mathrm{5}}^{\mathrm{2}}} \right)}^{\mathrm{2}}}\]
\[\begin{align} & \mathrm{(a)125} \\ & \mathrm{(b)625} \\ & \mathrm{(c)25} \\ & \mathrm{(d)0} \\ \end{align}\]
Ans:
The solution will be
\[\begin{align} & {{\left( {{5}^{2}} \right)}^{2}}={{5}^{4}} \\ & {{\left( {{5}^{2}} \right)}^{2}}=5\times 5\times 5\times 5 \\ & {{\left( {{5}^{2}} \right)}^{2}}=625 \\ \end{align}\]
5. Find the value of \[\mathrm{x}\], when \[{{\mathrm{2}}^{\mathrm{x}}}\mathrm{=}{{\mathrm{4}}^{\mathrm{4}}}\]
\[\begin{align} & \mathrm{(a)x=6} \\ & \mathrm{(b)x=2} \\ & \mathrm{(c)x=8} \\ & \mathrm{(d)x=-5} \\ \end{align}\]
Ans:
The solution will be
\[{{2}^{x}}={{4}^{4}}\]
\[\begin{align} & {{4}^{4}}={{\left( {{2}^{2}} \right)}^{4}} \\ & {{4}^{4}}={{2}^{8}} \\ \end{align}\]
\[{{2}^{x}}={{2}^{8}}\]
\[x=8\]
So the answer will be \[x=8\]
6. Find the value of \[{{\left( {{\mathrm{2}}^{\mathrm{11}}}\mathrm{+}{{\mathrm{6}}^{\mathrm{2}}}\mathrm{-}{{\mathrm{5}}^{\mathrm{1}}} \right)}^{\mathrm{0}}}\]
\[\begin{align} & \mathrm{(a)0} \\ & \mathrm{(b)-1} \\ & \mathrm{(c)1} \\ & \mathrm{(d)None} \\ \end{align}\]
Ans:
The solution will be
\[\begin{align} & {{\left( {{2}^{11}}+{{6}^{2}}-{{5}^{1}} \right)}^{0}}={{\left( anything \right)}^{0}} \\ & {{\left( {{2}^{11}}+{{6}^{2}}-{{5}^{1}} \right)}^{0}}=1 \\ \end{align}\]
So the solution will be
\[{{\left( {{2}^{11}}+{{6}^{2}}-{{5}^{1}} \right)}^{0}}=1\]
7.\[{{\mathrm{I}}^{\mathrm{3}}}\mathrm{+}{{\mathrm{I}}^{\mathrm{-3}}}\mathrm{=?}\] What is the solution?
\[\begin{align} & \mathrm{(a)2} \\ & \mathrm{(b)3} \\ & \mathrm{(c)-3} \\ & \mathrm{(d)None} \\ \end{align}\]
Ans:
The solution will be
\[\begin{align} & {{I}^{3}}+{{I}^{-3}}=\left( I\times I\times I \right)+\dfrac{1}{\left( I\times I\times I \right)} \\ & {{I}^{3}}+{{I}^{-3}}=\left( -I \right)+\dfrac{1}{\left( -I \right)} \\ & {{I}^{3}}+{{I}^{-3}}=\dfrac{-1+1}{\left( -I \right)} \\ & {{I}^{3}}+{{I}^{-3}}=0 \\ \end{align}\]
So the solution is (d)
Short Answer Questions 2 Marks
8. Follow the pattern and complete
Ans:
The pattern for the solution is square root of the numbers which continue as
\[\begin{align} & 1234321={{1111}^{2}} \\ & 123454321={{11111}^{2}} \\ \end{align}\]
9. If \[{{\mathrm{2}}^{\mathrm{x}}}\mathrm{ }\!\!\times\!\!\text{ }{{\mathrm{5}}^{\mathrm{x}}}\mathrm{=1000}\] then \[\mathrm{x=?}\]
Ans:
For solving we will just factorise
\[\begin{align} & {{2}^{x}}\times {{5}^{x}}=1000 \\ & {{2}^{x}}\times {{5}^{x}}=5\times 5\times 5\times 2\times 2\times 2 \\ & {{2}^{x}}\times {{5}^{x}}={{2}^{3}}\times {{5}^{3}} \\ & x=3 \\ \end{align}\]
10.Find\[{{\mathrm{3}}^{\mathrm{4}}}\mathrm{+}{{\mathrm{4}}^{\mathrm{3}}}\mathrm{+}{{\mathrm{5}}^{\mathrm{3}}}\] and give the answers in cube
Ans:
Solve the expression
\[\begin{align} & {{3}^{4}}+{{4}^{3}}+{{5}^{3}}=27+64+125 \\ & {{3}^{4}}+{{4}^{3}}+{{5}^{3}}=216 \\ & {{3}^{4}}+{{4}^{3}}+{{5}^{3}}=6\times 6\times 6 \\ & {{3}^{4}}+{{4}^{3}}+{{5}^{3}}={{6}^{3}} \\ \end{align}\]
11. Find the missing number \[\mathrm{x}\] in \[{{\mathrm{5}}^{\mathrm{2}}}\mathrm{+}{{\mathrm{x}}^{\mathrm{2}}}\mathrm{=1}{{\mathrm{3}}^{\mathrm{2}}}\]
Ans:
Solve the expression
\[\begin{align} & {{5}^{2}}+{{x}^{2}}={{13}^{2}} \\ & 25+{{x}^{2}}=169 \\ & {{x}^{2}}=144 \\ & x=\sqrt{144} \\ & x=12 \\ \end{align}\]
12. Simplify in exponent form \[\left( {{\mathrm{3}}^{\mathrm{4}}}\mathrm{ }\!\!\times\!\!\text{ }{{\mathrm{3}}^{\mathrm{2}}} \right)\mathrm{ }\!\!\div\!\!\text{ }{{\mathrm{3}}^{\mathrm{-4}}}\]
Ans:
Solve the expression
\[\begin{align} & \left( {{3}^{4}}\times {{3}^{2}} \right)\div {{3}^{-4}}=\dfrac{{{3}^{4+2}}}{{{3}^{-4}}} \\ & \left( {{3}^{4}}\times {{3}^{2}} \right)\div {{3}^{-4}}=\dfrac{{{3}^{6}}}{{{3}^{-4}}} \\ & \left( {{3}^{4}}\times {{3}^{2}} \right)\div {{3}^{-4}}={{3}^{6+4}} \\ & \left( {{3}^{4}}\times {{3}^{2}} \right)\div {{3}^{-4}}={{3}^{10}} \\ \end{align}\]
13. Expand
\[\begin{align} & \mathrm{(a)1526}\mathrm{.26} \\ & \mathrm{(b)8379} \\ \end{align}\]Using exponents
Ans:
Solve in exponential form
\[\begin{align} & (a)1526.26=1\times {{10}^{3}}+5\times {{10}^{2}}+2\times {{10}^{1}}+6\times {{10}^{\circ }}+2\times {{10}^{-1}}+6\times {{10}^{-2}} \\ & (b)8379=8\times {{10}^{3}}+3\times {{10}^{2}}+7\times {{10}^{1}}+9\times {{10}^{0}} \\ \end{align}\]
14. Simplify using laws of exponents
\[\begin{align} & \mathrm{(a)}\dfrac{\mathrm{1}}{\mathrm{9}}\mathrm{ }\!\!\times\!\!\text{ }{{\mathrm{3}}^{\mathrm{5}}} \\ & \mathrm{(b)}{{\mathrm{5}}^{\mathrm{a}}}\mathrm{ }\!\!\times\!\!\text{ 2}{{\mathrm{5}}^{\mathrm{b}}} \\ \end{align}\]
Ans:
Solve in exponential form
\[\begin{align} & (a)\dfrac{1}{9}\times {{3}^{5}}=\dfrac{{{3}^{5}}}{9}=\dfrac{{{3}^{5}}}{{{3}^{2}}}={{3}^{5-2}}={{3}^{3}}=27 \\ & (b){{5}^{a}}\times {{25}^{b}}={{5}^{a}}\times {{\left( {{5}^{2}} \right)}^{b}}={{5}^{a}}\times {{5}^{b}}={{5}^{a+2b}} \\ \end{align}\]
15. Express the following number as a product of powers of prime factors.
\[\begin{align} & \mathrm{(a)1225} \\ & \mathrm{(b)3600} \\ \end{align}\]
Ans:
Solve in exponential form
\[\begin{align} & (a)1225=5\times 5\times 7\times 7 \\ & 1225={{5}^{2}}\times {{7}^{2}} \\ \end{align}\]
\[\begin{align} & (b)3600=2\times 2\times 2\times 2\times 3\times 3\times 5\times 5 \\ & 3600={{2}^{4}}\times {{3}^{2}}\times {{5}^{2}} \\ \end{align}\]
16. Express the following large no’s in its scientific notation.
\[\begin{align} & \mathrm{(a)650200000000} \\ & \mathrm{(b)301000000} \\ \end{align}\]
Ans:
Solve in exponential form
\[(a)650200000000=6.502\times {{10}^{11}}\]
\[(b)301000000=3.01\times {{10}^{8}}\]
17. Express the following in expanded form \[\begin{align} & \mathrm{(a)1}\mathrm{.682 }\!\!\times\!\!\text{ 1}{{\mathrm{0}}^{\mathrm{5}}} \\ & \mathrm{(b)0}\mathrm{.86 }\!\!\times\!\!\text{ 1}{{\mathrm{0}}^{\mathrm{4}}} \\ \end{align}\]
Ans:
Solve in exponential form
\[\begin{align} & (a)168200 \\ & (b)8600 \\ \end{align}\]
Short Answer Questions 3 Marks
18. State true or false
$\begin{align} & \mathrm{(a)}\left( \mathrm{1}{{\mathrm{0}}^{\mathrm{0}}}\mathrm{+1}{{\mathrm{2}}^{\mathrm{0}}} \right)\left( \mathrm{1}{{\mathrm{6}}^{\mathrm{0}}}\mathrm{+1}{{\mathrm{2}}^{\mathrm{0}}} \right)\mathrm{}{{\mathrm{8}}^{\mathrm{2}}} \\ & \mathrm{(b)}{{\left( {{\mathrm{3}}^{\mathrm{4}}} \right)}^{\mathrm{2}}}\mathrm{=}{{\mathrm{3}}^{\mathrm{8}}} \\ & \mathrm{(c)}{{\left( {{\mathrm{5}}^{\mathrm{2}}} \right)}^{\mathrm{3}}}\mathrm{=100000} \\ \end{align}$
Ans:
(a) False
(b) True
(c) False
19. Simplify \[\dfrac{{{\mathrm{5}}^{\mathrm{2}}}\mathrm{ }\!\!\times\!\!\text{ }{{\mathrm{a}}^{\mathrm{-4}}}}{{{\mathrm{5}}^{\mathrm{-3}}}\mathrm{ }\!\!\times\!\!\text{ 10 }\!\!\times\!\!\text{ }{{\mathrm{a}}^{\mathrm{-8}}}}\] , where \[\mathrm{a}\ne \mathrm{0}\]
Ans:
Solve the expression
\[\begin{align} & \dfrac{{{5}^{2}}\times {{a}^{-4}}}{{{5}^{-3}}\times 10\times {{a}^{-8}}}={{5}^{2}}\times {{a}^{-4}}\times {{5}^{3}}\times 10\times {{a}^{8}} \\ & =\left( {{5}^{2}}\times {{5}^{3}} \right)\times \left( {{a}^{8}}\times {{a}^{-4}} \right)\times 10 \\ & =\left( {{5}^{2+3}} \right)\left( {{a}^{8-4}} \right)\times 10 \\ & ={{5}^{5}}\times {{a}^{4}}\times 10 \\ & \dfrac{{{5}^{2}}\times {{a}^{-4}}}{{{5}^{-3}}\times 10\times {{a}^{-8}}}=10{{(a)}^{4}}{{(5)}^{5}} \\ \end{align}\]
20. Find the area of the square attached to the hypotenuse in the diagram. Express the solution in exponential form.
Ans:
From Pythagoras theorem
\[\begin{align} & Are{{a}_{(longside)}}={{A}_{side1}}+{{A}_{side2}} \\ & A={{5}^{2}}+{{12}^{2}} \\ & A=169 \\ & A={{13}^{2}}c{{m}^{2}} \\ \end{align}\]
21.Simplify\[\left[ \left\{ {{\left( \dfrac{\mathrm{1}}{\mathrm{3}} \right)}^{\mathrm{-3}}}\mathrm{-}{{\left( \dfrac{\mathrm{1}}{\mathrm{2}} \right)}^{\mathrm{-3}}}\mathrm{ }\!\!\div\!\!\text{ }{{\left( \dfrac{\mathrm{1}}{\mathrm{5}} \right)}^{\mathrm{-2}}} \right\} \right]\]
Ans:
Solve the expression
\[\begin{align} & \left[ \left\{ {{\left( \dfrac{1}{3} \right)}^{-3}}-{{\left( \dfrac{1}{2} \right)}^{-3}}\div {{\left( \dfrac{1}{5} \right)}^{-2}} \right\} \right] \\ & =\left[ \dfrac{{{1}^{-3}}}{{{3}^{-3}}}-\dfrac{{{1}^{-3}}}{{{2}^{-3}}}\div \dfrac{{{1}^{-2}}}{{{5}^{-2}}} \right] \\ & =\left[ \left( \dfrac{{{3}^{3}}}{{{1}^{3}}}-\dfrac{{{2}^{3}}}{{{1}^{3}}} \right)\div \dfrac{{{5}^{2}}}{{{1}^{2}}} \right] \\ & =\left( \dfrac{27}{1}-\dfrac{8}{1} \right)\div 25 \\ & =\dfrac{(27-8)}{25} \\ & =\dfrac{19}{25} \\ \end{align}\]
22. if \[\mathrm{x=}{{\left( \dfrac{\mathrm{5}}{\mathrm{2}} \right)}^{\mathrm{2}}}\mathrm{ }\!\!\times\!\!\text{ }{{\left( \dfrac{\mathrm{2}}{\mathrm{5}} \right)}^{\mathrm{-3}}}\] find the value of \[{{\mathrm{x}}^{\mathrm{-2}}}\]
Ans:
\[\begin{matrix} x={{\left( \dfrac{5}{2} \right)}^{2}}\times {{\left( \dfrac{2}{5} \right)}^{-3}} \\ x={{\left( \dfrac{5}{2} \right)}^{2}}\times \dfrac{{{5}^{3}}}{{{2}^{3}}} \\ x=\dfrac{{{5}^{4}}}{{{2}^{4}}}={{\left( \dfrac{5}{2} \right)}^{4}} \\ \end{matrix}\]
The value of \[{{x}^{-2}}={{\left[ {{\left( \dfrac{5}{2} \right)}^{4}} \right]}^{-2}}\]
\[\begin{align} & {{x}^{-2}}={{\left[ {{\left( \dfrac{5}{2} \right)}^{4}} \right]}^{-2}} \\ & {{x}^{-2}}={{\left( \dfrac{5}{2} \right)}^{4\times (-2)}} \\ & {{x}^{-2}}={{\left( \dfrac{5}{2} \right)}^{-8}} \\ & {{x}^{-2}}={{\left( \dfrac{2}{5} \right)}^{8}} \\ \end{align}\]
23. Prove that \[{{\left[ {{\left( \dfrac{\mathrm{1}}{\mathrm{2}} \right)}^{\mathrm{2}}} \right]}^{\mathrm{3}}}\mathrm{ }\!\!\times\!\!\text{ }{{\left( \dfrac{\mathrm{1}}{\mathrm{3}} \right)}^{\mathrm{-4}}}\mathrm{ }\!\!\times\!\!\text{ }{{\mathrm{3}}^{\mathrm{-2}}}\mathrm{ }\!\!\times\!\!\text{ }\dfrac{\mathrm{1}}{\mathrm{6}}\mathrm{=}\dfrac{\mathrm{3}}{\mathrm{128}}\]
Ans:
Solve the left hand side and equate with the right
\[\begin{align} & LHS={{\left[ {{\left( \dfrac{1}{2} \right)}^{2}} \right]}^{3}}\times {{\left( \dfrac{1}{3} \right)}^{-4}}\times {{3}^{-2}}\times \dfrac{1}{6} \\ & ={{\left( \dfrac{{{1}^{2}}}{{{2}^{2}}} \right)}^{3}}\times {{\left( {{3}^{-1}} \right)}^{-4}}\times {{3}^{-2}}\times \dfrac{1}{2}\times \dfrac{1}{3} \\ & =\dfrac{1}{{{2}^{6}}}\times {{3}^{4}}\times {{3}^{-2}}\times \dfrac{1}{2}\times {{3}^{-1}} \\ & =\dfrac{1}{{{2}^{7}}}\times {{3}^{4-3}} \\ & =\dfrac{3}{128} \\ \end{align}\]
24. A dish holds \[\mathbf{100}\] bacteria. It is known that the bacteria double in number every hour.
How many bacteria will be present after each number of hours?
\[\begin{align} & \mathrm{(a)1} \\ & \mathrm{(b)5} \\ & \mathrm{(c)n} \\ & \mathrm{(d)}\dfrac{\mathrm{3}}{\mathrm{2}} \\ \end{align}\]
Ans:
Number of hours will multiply with the number of bacteria two the power of two
\[\begin{align} & (a)100\left( {{2}^{1}} \right)=200 \\ & (b)100\left( {{2}^{5}} \right)=100\left( 32 \right) \\ & 100\left( {{2}^{5}} \right)=3200 \\ & (c)100\left( {{2}^{n}} \right) \\ & (d)100\left( {{2}^{\dfrac{3}{2}}} \right) \\ \end{align}\]
25. What is the area of the rectangle with the width of \[\mathrm{6}{{\mathrm{x}}^{\mathrm{2}}}\]and the length of\[\mathrm{12}{{\mathrm{x}}^{\mathrm{3}}}\]? After finding the area, find the solution at \[\mathrm{x=2m}\] .
Ans:
\[Area\text{ }of\text{ }rectangle\text{ }=\text{ }length\times ~breadth\]
\[\begin{align} & A=12{{x}^{3}}\times 6{{x}^{2}} \\ & A=72{{x}^{5}} \\ & at,x=2m \\ & A=72\times {{\left( 2 \right)}^{5}} \\ & A=72\times 32 \\ & A=2304{{m}^{2}} \\ \end{align}\]
Class 8 Maths Exponents and Powers Important Questions
The Exponents and Powers Class 8 Important Questions are also available in the PDF format which students can download on their devices and access offline as per their convenient time. With these questions in hand, students will surely get a better conceptual understanding and learn how to divide their time into more important topics than the less significant ones. The questions are based on the topics that are outlined below.
List of Formulas of Class 8 Maths Chapter 10 Exponents and Powers
Find here the list of all important formulas discussed in the chapter. Students can solve all the questions asked in the chapter using the formulas given below.
Practice Questions of Chapter 10 Exponents and Powers
For more practice, we have provided some practise questions for the students. Try to solve these questions.
What is the value of 90?
What is the value of 143/53?
Find the value of 75 x 95.
Find the value of (62)3.
Evaluate the value of 87 x 85.
These questions are very beneficial for the students. Practice the important questions along with the practice question given above. These questions are solved by the subject-matter experts following the pattern of CBSE guidelines.
Why are Important Questions for Class 8 Maths Chapter 10 - Exponents and Powers Necessary?
Important questions in Vedantu's Class 8 Maths Chapter 10 - Exponents and Powers help reinforce key concepts covered in the chapter.
They serve as a targeted study resource for students preparing for exams, as they often focus on the types of questions commonly found in examinations.
These questions are designed to challenge students' problem-solving skills, promoting a deeper understanding of the topic.
Students can use these questions to self-assess their understanding of the chapter, identifying areas that may need further review.
By practising important questions, students can improve their time management skills, essential for completing exams within the allocated time.
These questions often involve the application of theoretical knowledge to practical problems, enhancing the student's ability to apply concepts in different scenarios.
Regular practice with important questions can boost a student's confidence, helping them approach exams with a more positive mindset.
Important questions typically cover a range of topics within the chapter, ensuring a comprehensive review of the material.
For students aspiring to pursue further studies or competitive exams, practising these questions can be valuable in building a strong foundation in mathematics.
Tips to learn Class 8 Maths Chapter 10 Exponents and Powers using Important Questions
Before solving questions, get clear on concepts like laws of exponents, negative exponents, and standard form. This foundation makes it easier to tackle problems.
Focus on the key formulas, like multiplying or dividing exponents and simplifying powers. Write them down and practice their application in different types of questions.
When working on important questions, break the problem into smaller steps. Don’t rush; focus on accuracy to avoid mistakes.
Practice a variety of problems, including MCQs, short answers, and word problems. This will prepare you for different question formats in exams.
After solving questions, check your answers carefully. Understand any mistakes and revisit the concepts behind them to improve.
Conclusion
Chapter 10 of CBSE Class 8 Maths focuses on Exponents and Powers, which are essential concepts in understanding how numbers grow when raised to different powers. Key topics include laws of exponents, such as product rule, quotient rule, and power rule, which help simplify expressions with powers. Students also learn how to express large numbers in scientific notation and calculate values for negative exponents. Mastering these concepts is crucial for solving complex mathematical problems. Overall, this chapter helps build a strong foundation for understanding higher-level mathematics and problem-solving in various real-world scenarios.
Related Study Materials for CBSE Class 8 Maths Chapter 10
CBSE Class 8 Maths Chapter-wise Important Questions
Other Important Related Links for CBSE Class 8 Maths
FAQs on CBSE Important Questions for Class 8 Maths Exponents and Powers - 2025-26
1. What are some of the most frequently asked 1-mark important questions from CBSE Class 8 Maths Chapter 10, Exponents and Powers?
For the 2025-26 exams, students should focus on single-step questions for 1 mark. These typically include finding the value of expressions with negative exponents (e.g., find the value of 3-2), applying the zero exponent rule (e.g., what is (60 + 50)?), or finding the multiplicative inverse of a number with a power.
2. Which laws of exponents are crucial for solving important questions from this chapter?
To score well, it is essential to master the following laws of exponents as they are used in almost all simplification problems:
- Product of Powers: am × an = am+n
- Quotient of Powers: am ÷ an = am-n
- Power of a Power: (am)n = amn
- Product of Powers with Same Exponent: am × bm = (ab)m
- Quotient of Powers with Same Exponent: am ÷ bm = (a/b)m
- Zero Exponent: a0 = 1 (for any non-zero 'a')
- Negative Exponent: a-m = 1/am
3. How are questions on expressing numbers in standard form tested in the Class 8 Maths exam?
Questions on standard form (or scientific notation) are very important and usually ask you to perform one of two tasks. You may be given a very large or very small number (e.g., 0.0000057 or 149,600,000) and asked to write it in the form k × 10n, where 1 ≤ k < 10. Alternatively, you might be given the standard form and asked to convert it back to its usual form.
4. What kind of High Order Thinking Skills (HOTS) questions can be expected from Exponents and Powers?
HOTS or difficult questions from this chapter often require applying multiple laws of exponents in a single problem to find the value of an unknown variable. For example, you might be asked to find the value of 'x' in an equation like (5/7)-3 × (5/7)-9 = (5/7)3x. Solving this requires first simplifying the left side using the product rule and then equating the exponents.
5. For the 2025-26 board exams, what type of simplification problems can be expected for 3 marks?
For 3 marks, expect multi-step simplification problems that test your knowledge of negative exponents and at least two or three laws of exponents combined. A typical important question would be to evaluate an expression like [(1/3)-2 - (1/2)-3] ÷ (1/4)-2. These questions test your ability to handle operations in the correct order.
6. Why is it that any non-zero number raised to the power of zero is 1?
This is a fundamental rule that stems from the division law of exponents. Consider the expression am / am. According to the division rule, this simplifies to a(m-m) = a0. However, we also know that any non-zero number divided by itself is equal to 1. Therefore, by comparing the two results, we can conclude that a0 = 1.
7. What is the most common mistake students make when simplifying expressions with exponents?
A very common mistake is confusing the rules for multiplying powers with the same base versus powers with the same exponent. Students often incorrectly multiply the bases when they should be adding the exponents. For example, for 23 × 24, the correct answer is 2(3+4) = 27, not 47. Always check if the bases are the same or if the exponents are the same before applying a law.
8. How do I solve questions where I need to find the value of a reciprocal with a negative exponent?
This is a common type of important question. First, find the value of the base expression. For example, to find the reciprocal of (2/5)-2, first evaluate it. (2/5)-2 becomes (5/2)2, which is 25/4. The reciprocal is simply this value flipped, which would be 4/25. Do not take the reciprocal of the base before handling the negative exponent.
