# Laws of Exponents

How to simplify expressions using the laws of exponents

### Video on the Laws of Exponents

##### Examples

Division:
Exponent to an exponent:

### Practice Problems

Since we are multiplying exponents we add the exponents:

$x^3 \times x^2 = x^{3+2} = x^5$

Use the power rule of exponents and multiply exponents:

$(x^3) ^2 = x^{(3 \times 2)}= x^6$

Use the quotient rule of exponents and subtract the exponents:

$\frac {x^5}{ x^3} = x^{(5 - 3)}= x^2$

Since we are multiplying exponents we add the exponents

$x^{11} \times x^5 = x^{11+5} = x^{16}$

You cannot simplify this expression! Remember that all of the rules on this page only work when the exponents have the same base!

### Rules and Laws Covered elsewhere

#### Negative Exponents

Negative exponents are explained separately here.

#### Fraction Exponents

Fraction exponents are explained separately here

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