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## Multiplying Exponents

#### Introduction

Multiplying exponents is quite straightforward. When the bases are the same, we simply add the first exponent to the second exponent.

#### Terms

Exponent - The number of times to multiply the base.
Base - The number being multiplied.

## Lesson

To multiply exponents with the same base, we add all the exponents together. For example, if we are given $2^6 * 2^2$, we add the exponents – 6+2=8 and we are left with $2^8$ or 256 (evaluated).

Here is another example:

$3^3 * 3^4 = 3^{3+4} = 3^7 = 2187$

## Examples

#### Multiplying Exponents (Example #1)

$x^{2}x^{-1}x^{-2}$
When multiplying exponents with the same base, you add the exponents
$x^{2}x^{-1}x^{-2} = x^{2-1-2}$
$x^{2-1-2} = x^{-1}$

#### Multiplying Exponents (Example #2)

$s^{1}s^{2}s^{3}$
When multiplying exponents with the same base, you add the exponents
$s^{1}s^{2}s^{3} = s^{1+2+3}$
$s^{1+2+3} = s^{6}$

#### Multiplying Exponents (Example #3)

$4^{-2}4^{1}$
When multiplying exponents with the same base, you add the exponents
$4^{-2}4^{1} = 4^{-2+1}$
$4^{-2+1} = 4^{-1}$

#### Multiplying Exponents (Example #4)

$3^{5}3^{-1}3^{2}$
When multiplying exponents with the same base, you add the exponents
$3^{5}3^{-1}3^{2} = 3^{5-1+2}$
$3^{5-1+2} = 3^{6}$