Question

Briefly explain Exponents and powers

Answer 1

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Laws of Exponents

The laws of exponents are explained here along with their examples.

1. Multiplying powers with same base

For example: x² × x³, 2³ × 2⁵, (-3)² × (-3)⁴

In multiplication of exponents if the bases are same then we need to add the exponents.


Consider the following: 

1. 2³ × 2²= (2 × 2 × 2) × (2 × 2) = 23+2 = 2⁵


2. 3⁴ × 3² = (3 × 3 × 3 × 3) × (3 × 3) = 34+2 = 3⁶

3. (-3)³ × (-3)⁴ = [(-3) × (-3) × (-3)] × [(-3) × (-3) × (-3) × (-3)] = (-3)3+4 = (-3)⁷


4. m⁵ × m³ = (m × m × m × m × m) × (m × m × m) = m5+3 = m⁸


From the above examples, we can generalize that during multiplication when the bases are same then the exponents are added. 

aᵐ × aⁿ = am+n

In other words, if ‘a’ is a non-zero integer or a non-zero rational number and m and n are positive integers, then

aᵐ × aⁿ = am+n

Similarly, (a/b)ᵐ × (a/b)ⁿ = (a/b)m+n

Note: 

(i) Exponents can be added only when the bases are same. 

(ii) Exponents cannot be added if the bases are not same like

m⁵ × n⁷, 2³ × 3⁴

For example:

1. 5³ ×5⁶

= (5 × 5 × 5) × (5 × 5 × 5 × 5 × 5 × 5) 

= 53+6, [here the exponents are added] 

= 5⁹

Answer 2

exponent means the quality that representing the power of a no. or expression is to be raised......
and
power is an expression that represents repeated multiplication of the same factor.......


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