Multiplying Exponents with Difference Base and Same Powers

In this tutorial, we will learn the rule of multiplication of exponents with different bases but same powers.

When we multiply exponents with different bases and same powers, we can simply multiply the bases and keep the exponent same.

Mathematically it can be written as,

[ aⁿ  x  bⁿ = (a x b)ⁿ ]

Let two exponents with a different base and same power is aⁿ and bⁿ.

Here a and b are the different bases and n is the power of both a and b.

The general form of this rule is

Example: (2)² x (3)²

Example: (3 x 2)⁵

= (3 x 3 x 3 x 3 x 3)⁵ x (2 x 2 x 2 x 2 x 2)⁵

Here, exponents are same as 5 but bases are different that’s are 3 and 2.

= (3 x 2) x (3 x 2) x (3 x 2) x (3 x 2) x (3 x 2) [5 times]

= 6 x 6 x 6 x 6 x 6

= 7776

Example: (3 x q)⁴

= (3 x 3 x 3 x 3)⁴ x (q x q x q x q)⁴

Here, exponents are same as 4 but bases are different that’s are 3 and q.

= (3 x q) x (3 x q) x (3 x q) x (3 x q)

= 81q⁴

Example: = (7)³ x (5)³

= (7 x 5)³

= (7 x 5) x (7 x 5) x (7 x 5)

= (35)³

= (35 x 35 x 35)

= (35 x 35 x 35)

= 82875

Note : When multiplying two exponents with same powers and different bases, the bases are multiplied.