Multiplying Variables with Exponents – Rule – Examples

Multiplication of variables with exponents

In this tutorial, we will learn the multiplication of variable with exponents.

If the base of a term is a variable, we use the same rules of multiplication that are used for numbers.

When the variable bases are same, the powers are added.

Example: Solve (a)² x (a)³

Solution: Here, variable base is same, that is a. So, we will add the exponents.

Thus, (a)² x (a)³

= (a)²⁺³

= (a)⁵

When the variable bases are different and the powers are same, the bases are multiplied first.

Example: (a)³ x (b)³

Solution: Here, variable base are different and powers are same, that is a. So, we will multiplied the bases.

(a)³ x (b)³

= (a x b)³

= (ab)³

When the variable bases and powers are different, the exponents are evaluated separately and then multiplied.

Example: (a)³ x (b)⁴

Solution: The variable bases and powers are different that is (a)³ x (b)⁴

Thus, (a)³ x (b)⁴

= (a)³ x (b)⁴