Question

i want an explanation on laws of exponents

Answer 1

Laws of Exponents:-When multiplying like bases, keep the base the same and add theexponents. When raising a base with a power to another power, keep the base the same and multiply the exponents. When dividing like bases, keep the base the same and subtract the denominator exponent from the numerator exponent.

hope this helps.....☺️

Answer 2

Hi there,

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

 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+23+2 = 2⁵

2. 3⁴ × 3² = (3 × 3 × 3 × 3) × (3 × 3) = 34+24+2 = 3⁶

3. (-3)³ × (-3)⁴ = [(-3) × (-3) × (-3)] × [(-3) × (-3) × (-3) × (-3)] = (-3)3+43+4 = (-3)⁷

4. m⁵ × m³ = (m × m × m × m × m) × (m × m × m) = m5+35+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.

Hope this helps!

 Thank you..