How do you evaluate the expression 4^-7/4^-3 using the properties?

May 30, 2017

See a solution process below:

Explanation:

We can use this rule of exponents to simplify the expression:

${x}^{\textcolor{red}{a}} / {x}^{\textcolor{b l u e}{b}} = \frac{1}{x} ^ \left(\textcolor{b l u e}{b} - \textcolor{red}{a}\right)$

${4}^{\textcolor{red}{- 7}} / {4}^{\textcolor{b l u e}{- 3}} \implies \frac{1}{4} ^ \left(\textcolor{b l u e}{- 3} - \textcolor{red}{- 7}\right) \implies \frac{1}{4} ^ \left(\textcolor{b l u e}{- 3} + \textcolor{red}{7}\right) \implies \frac{1}{4} ^ 4 \implies \frac{1}{256}$

May 30, 2017

${4}^{-} 4$

$= \frac{1}{256}$

Explanation:

The problem can be written as ${4}^{- 7 - \left(- 3\right)}$ because when you divide exponentials, you subtract them.

=${4}^{- 7 + 3}$

=${4}^{-} 4$

However, the indices should be positive in the answer.

$= \frac{1}{4} ^ 4$

$= \frac{1}{256}$