# Product of Powers

How to solve the product of powers a^{m}⋅a^{n}: formula, 2 examples, and their solutions.

## Formula

a^{m}⋅a^{n} = a^{m + n}

When multiplying the same base powers,

add the exponents (m + n).

## Examplex^{6}⋅x^{8}

Solution

Solution (Detail)

x^{6} and x^{8} have the same base: x.

So x^{6}⋅x^{8} = x^{6 + 8}.

6 + 8 = 14.

So x^{14} is the answer.

## Example(3^{2}xy^{4})⋅(3x^{3}y^{7})

Solution

Solution (Detail)

3^{2} and 3 have the same base: 3.

So 3^{2}⋅3 = 3^{2 + 1}.

x and x^{3} have the same base: x.

So x⋅x^{3} = x^{1 + 3}.

y^{4} and y^{7} have the same base: y.

So y^{4}⋅y^{7} = y^{4 + 7}.

So (given) = 3^{2 + 1}⋅x^{1 + 3}⋅y^{4 + 7}.

The same base powers are combined.

Simplify the exponents.

2 + 1 = 3

1 + 3 = 4

4 + 7 = 11

3^{3} = 27

So 27x^{4}y^{11} is the answer.