# How do you use the laws of exponents to simplify the expression  ((4^2)/(4^3))*(4)^-3?

May 21, 2018

$\frac{1}{256}$

#### Explanation:

$\text{using the "color(blue)"laws of exponents}$

•color(white)(x)a^m/a^nhArra^((m-n))

•color(white)(x)a^mxxa^nhArra^((m+n))

•color(white)(x)a^-mhArr1/a^m

$\Rightarrow \left({4}^{2} / {4}^{3}\right) \times {4}^{-} 3$

$= {4}^{\left(2 - 3\right)} \times {4}^{-} 3$

$= {4}^{-} 1 \times {4}^{-} 3$

$= {4}^{\left(- 1 + \left(- 3\right)\right)} = {4}^{-} 4 = \frac{1}{4} ^ 4 = \frac{1}{256}$

May 21, 2018

$\frac{1}{4} ^ 4 \mathmr{and} {4}^{-} 4$

#### Explanation:

When dividing like terms with powers you subtract the powers.

${4}^{2} / {4}^{3} = {4}^{2 - 3} = {4}^{- 1}$

When multiplying like terms with powers you add the powers

$\left({4}^{2} / {4}^{3}\right) \times {4}^{-} 3 = {4}^{- 1} \times {4}^{-} 3 = {4}^{- 1 + - 3} {4}^{- 1 - 3} = {4}^{-} 4$