# How do you simplify (25b^6)^-1.5?

Apr 29, 2017

See the entire solution process below:

#### Explanation:

First, use these rules of exponents to remove the outer exponent:

$a = {a}^{\textcolor{red}{1}}$ and ${\left({x}^{\textcolor{red}{a}}\right)}^{\textcolor{b l u e}{b}} = {x}^{\textcolor{red}{a} \times \textcolor{b l u e}{b}}$

${\left(25 {b}^{6}\right)}^{-} 1.5 = {\left({25}^{\textcolor{red}{1}} {b}^{\textcolor{red}{6}}\right)}^{\textcolor{b l u e}{- 1.5}} = {25}^{\textcolor{red}{1} \times \textcolor{b l u e}{- 1.5}} {b}^{\textcolor{red}{6} \times \textcolor{b l u e}{- 1.5}} =$

${25}^{-} 1.5 {b}^{-} 6.5$

We can now use this rule of exponents to eliminate the negative exponents:

${25}^{\textcolor{red}{- 1.5}} {b}^{\textcolor{red}{- 6.5}} = \frac{1}{{25}^{\textcolor{red}{- - 1.5}} {b}^{\textcolor{red}{- - 6.5}}} = \frac{1}{{25}^{1.5} {b}^{6.5}}$

We can change the fractions to fractions as follows:

$\frac{1}{{25}^{1.5} {b}^{6.5}} = \frac{1}{{25}^{\frac{3}{2}} {b}^{\frac{13}{2}}}$

We can rewrite this expression as:

$\frac{1}{{25}^{\frac{1}{2} \times 3} {b}^{6.5}}$

We can rewrite this as:

$\frac{1}{{\left({25}^{\frac{1}{2}}\right)}^{3} {b}^{6.5}} = \frac{1}{{5}^{3} {b}^{6.5}} = \frac{1}{125 {b}^{6.5}}$