Cbse Class 7 Maths Notes Chapter 11

1. Exponents:

Exponents are used to convey huge numbers in a more readable, understandable, comparable, and manipulable format.

2. Expressing Large Numbers in the Standard Form:

• Any number between $1.0$ and $10.0$ (including $1.0$) multiplied by a power of ten can be expressed as a decimal number between $1.0$ and $10.0$(including $1.0$).

• The standard form of a number is also known as scientific motion.

3. Large numbers are difficult to read, comprehend, compare, and manipulate. 

4. We use exponents to make all of this easier by transforming many of the enormous numbers into a shorter form.

5. What are some examples of exponential forms of numbers?

$100={{10}^{2}}$ (It can be read as $10$ raised to $2$)

$512={{8}^{3}}$

$243={{3}^{5}}$

Here, $\text{10, 8}$ and $3$ are the bases, whereas $\text{2, 3}$ and $5$ are their respective exponents.

We also can say that

$100$ is the ${{\text{2}}^{\text{nd}}}$ power of $\text{10}$ , 

$512$ is the ${{3}^{\text{rd}}}$ power of $8$ , 

$243$ is the ${{5}^{th}}$ power of $\text{3}$ , etc.

6. For any non-zero integers $\text{a}$ and $\text{b}$, and whole numbers $\text{m}$ and $\text{n}$, numbers in exponential form obey the following laws:

a. ${{\text{a}}^{\text{m}}}\text{  }\!\!\times\!\!\text{  }{{\text{a}}^{\text{n}}}\text{ = }{{\text{a}}^{\text{m+n}}}$

b. ${{\text{a}}^{\text{m}}}\text{  }\!\!\div\!\!\text{  }{{\text{a}}^{\text{n}}}\text{ = }{{\text{a}}^{\text{m-n}}}\text{ , m  n}$

c. ${{\left( {{\text{a}}^{\text{m}}} \right)}^{n}}\text{ = }{{\text{a}}^{\text{mn}}}$

d. ${{\text{a}}^{\text{m}}}\text{  }\!\!\times\!\!\text{  }{{\text{b}}^{m}}\text{ = }{{\left( ab \right)}^{\text{m}}}$

e. ${{\text{a}}^{\text{m}}}\text{ }\div \text{ }{{\text{b}}^{m}}\text{ = }{{\left( \dfrac{\text{a}}{b} \right)}^{\text{m}}}$

f. ${{\text{a}}^{0}}\text{ = 1}$

g. (-1)(even number) = 1

h. (-1)(odd number) = -1

Chapter Summary - Exponents and Powers

In "Exponents and Powers," Class 7 students explore the fascinating world of numbers with a special focus on making calculations simpler. Exponents, or small raised numbers, tell us how many times a number is multiplied by itself. For example, 2^3 means multiplying 2 by itself three times. This concept helps in handling large numbers more easily. Powers, on the other hand, are the results of using exponents. By understanding exponents and powers, students gain the superpower to simplify complex mathematical expressions and work with big numbers more conveniently. It's like discovering the secret code to unlock mathematical challenges!

Mnemonics to Easily Remember Chapter 11 - Exponents and Powers

Here are some simple mnemonics to help Class 7 students remember the key concepts of Exponents and Powers:

1. Rule Reminder: "Never Eat Slimy Worms" – Helps remember the order when applying exponents: Numbers, Exponents, Signs, and the final result, or 'Worms' (the solution).

2. Multiply Magic: "Two Elephants Ate Four Apples" – Indicates the process of multiplying the base number (2) by itself four times, corresponding to the exponent.

3. Exponent Expression: "Eshwar’s Power Escalates" – A fun way to remember that exponents show how a number's power increases.

4. Powers of 10: "Kangaroos Hopped Down Mountains Carrying Elephants" – A playful way to remember the increasing powers of 10.

5. Product Power: "My Elephant Jumped Over Three Walls" – Helps recall that exponent 3 means multiplying the base number (My Elephant) three times.

6. Squaring Shortcut: "Alia’s Cat Squared Its Tail" – A whimsical way to remember that squaring a number involves multiplying it by itself.

7. Cubing Clue: "Bheem Cubed Ice Perfectly" – Indicates that cubing involves multiplying a number by itself twice.

These mnemonics add a touch of creativity to make learning "Exponents and Powers" enjoyable and memorable for Class 7 students.

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Conclusion

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