# How do you simplify (5b^-3)^4 and write it using only positive exponents?

Aug 30, 2016

$= \frac{625}{b} ^ 12$

#### Explanation:

${\left(5 {b}^{-} 3\right)}^{4}$

$= {\left(\frac{5}{b} ^ 3\right)}^{4}$

$= \frac{625}{b} ^ 12$

Aug 30, 2016

${5}^{4} / {b}^{12} = \frac{625}{b} ^ 12$

#### Explanation:

There are 3 laws of indices being applied here,

A power outside applies to all the factors inside: ${\left(x y\right)}^{m} = {x}^{m} {y}^{m}$

Raising to a power, multiply the indices: ${\left({x}^{m}\right)}^{n} = {x}^{m n}$

Negative index becomes positive in the denominator and v.v.

${x}^{-} m = \frac{1}{x} ^ m$ or $\frac{1}{x} ^ - n = {x}^{n}$
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${\left(5 {b}^{-} 3\right)}^{4} = {5}^{4} {b}^{-} 12$

$= {5}^{4} / {b}^{12}$

This can also be written as $\frac{625}{b} ^ 12$