Multiplying Exponents- Same Base

In this chapter, we will study about multiplication of exponents with same base.

When a number repeatedly multiplied by itself, multiple times is known as Exponent.

For example: p raised to q means that p is multiplied by itself q times.

= p^q

= p x p x p x p x p…….q times.

Example: 4³ means multiply 4 by itself three times.

4³ = 4 x 4 x 4

Multiplying Exponents with Same Base

The general form of this rule is

When multiplying exponents with same base then exponents are added together and keep bases remains same.

Here, the base values are same as a, so keep them same and add the exponents (m+n) together.

Example: (i) 2² x 2⁴

= (2 x 2) x (2 x 2 x 2 x 2)

Here, the base values are same as three, so keep them same and add the exponents (2 +4), so the addition of exponents are (2 + 4 = 6).

= 2² x 2⁴ 

= 2^{2 + 4}

= 2⁶

2 x 2 x 2 x 2 x 2 x 2

= 2⁶

2⁶ = 64

Then multiply 2 by itself 6 times to get the answer.

Example: 2⁵ x 2⁷

= (2 x 2 x 2 x 2 x 2) x (2 x 2 x 2 x 2 x 2 x 2 x 2)

= 2⁵⁺⁷

= 2¹²

Example: (-5⁴) x (-5⁷)

= [(-5) x (-5) x (-5) x (-5)] x [(-5) x (-5) x (-5) x (-5) x (-5) x (-5) x (-5)]

= (-5)⁴⁺⁷

= (-5)¹¹

Example: (7/2)³ x (7/2)⁹

= [7/2 x (7/2) x (7/2)] x [(7/2) x (7/2) x (7/2) x (7/2) x (7/2) x (7/2) x (7/2) x (7/2) x (7/2)]

= (7/2)^{3 + 9}

= (7/2)¹²