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Class-7 Exponents

Introduction to Exponents

Power of a Negative Rational Number

Law of Exponents

Multiplication of Powers With Same Base

Division of Powers With Same Base

Zero Exponent

Power of a Power

Multiplication of Powers With Same Exponents

Division of Powers With Same Exponents

Negative Exponent

Exponents Test

Exponents Worksheet

Answer Sheet

Introduction to Exponents

Many a times we multiply same number multiple times. For example: 2 × 2 × 2 × 2 can be written as 24. Here 2 is known as base and 4 is known as exponents. We can read it as 2 to the power 4 or 2 power 4.

2 × 2 × 2 × 2 = 16 = 2⁴

Let's see some more examples.

Example 1. 3 × 3 × 3 × 3 × 3 = 3⁵ = 243

Example 2. 5 × 5 × 5 × 5 = 5⁴ = 625

Some power has special names, for example if the power of a number is 2 then it is named as square.

4² = 16 (It is read as 4 squared)

Similarly, if the power of a number is 3 then it is name cube.

3³ = 27 (It is read as 3 cubed)

Power of a Negative Rational Number

If power of a negative rational number is an odd natural number, then the result will be negative. If power of a negative rational number is an even natural number, then the result will be positive. Let's see some examples.

Example 1. Evaluate (−2)³.

Solution. (−2)³ = (−2) × (−2) × (−2) = −8

Example 2. Evaluate (−3)⁴.

Solution. (−3)⁴ = (−3) × (−3) × (−3) × (−3) = 81

Example 3. Evaluate (-23)³. Solution. (-23)³ = (-23) × (-23) × (-23)

        {(-2 × -2 × -2)(3×3×3)} = -827

Law of Exponents

There are 7 laws of exponents, they are mentioned below.

  1. Multiplication of powers with same base
  2. Division of powers with same base
  3. Zero exponent
  4. Power of a power
  5. Multiplication of powers with same exponents
  6. Division of powers with same exponents
  7. Negative exponent

Multiplication of Powers With Same Base

If 'p' is any rational number and a, b are natural numbers, then pa × pb = pa+b. Let's see some examples.

Example 1. Evaluate 23 × 22.

Solution. 23 × 22 = 2 × 2 × 2 × 2 × 2 = 25
In other words, we can write 23 x 22 = 23+2 = 25

Example 2. Evaluate (-2)3 × (-2)2.

Solution. (-2)3 × (-2)2 = {(-2) × (-2) × (-2)} × {(-2) × (-2)} = (-2)5
In other words, we can write (-2)3 x (-2)2 = (-2)3+2 = (-2)5

Division of Powers With Same Base

If 'p' is any rational number and a, b are natural numbers such that a > b, then pa ÷ pb = pa-b. Let's see some examples.

Example 1. Find the value of 35 ÷ 32.

Solution. 35 ÷ 32 = (3×3×3×3×3)(3×3) = 3 × 3 × 3 = 33

In other words, we can write 35 ÷ 32 = 35-2 = 33

Zero Exponent

If 'p' is any rational number, then p0 = 1. Let's see some examples.

Example 1. 25 ÷ 25 = (2×2×2×2×2)(2×2×2×2×2) = 3232 = 1

In other words, we can write 25 ÷ 25 = 25-5 = 20 = 1

Power of a Power

If 'p' is any rational number and 'a', 'b' are natural numbers, then (pa)b = pa×b. Let's see some example.

Example 1. Find the value of (32)3.

Solution. (32)3 = 32 × 32 × 32 = 32+2+2 = 36 = 32×3

So, we can assume that (32)3 = 32×3

Multiplication of Powers With Same Exponents

If 'p', 'q' are any rational numbers and 'a' is a natural number, then pa x qa = (pq)a. Let's see some example.

Example 1. Find the value of 23 × 33.

Solution. 23 × 33 = 2 × 2 × 2 × 3 × 3 × 3 = (2 × 3) × (2 × 3) × (2 × 3) = (2 × 3)3

Division of Powers With Same Exponents

If 'p', 'q' (q ≠ 0) are any rational numbers and 'a' is a natural number, then pa ÷ qa = (pq)a.

Example 1. Find the value of 23 ÷ 53.

Solution. 23 ÷ 53 = (2×2×2)(5×5×5) = 25 × 25 × 25 = (25)3

Example 2. Find the value of (-2)3 ÷ 73.

Solution. (-2)3 ÷ 73 = (-2 × -2 × -2)(7 × 7 × 7) = -27 × -27 × -27 = (-27)3

Negative Exponent

If 'p' is any non-zero rational number and 'n' is any natural number, then p-n= 1pn.

1pn = p0pn = p0-n = p-n
Hence it is proved that p-n= 1pn

Class-7 Exponents Test

Exponents - 1

Exponents - 2

Class-7 Exponents Worksheet

Exponents Worksheet - 1

Exponents Worksheet - 2

Exponents Worksheet - 3

Answer Sheet

Exponents-AnswerDownload the pdf










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