# How to simplify this?

## ${\left(\frac{16}{9 {x}^{4}}\right)}^{- \left(\frac{3}{2}\right)}$

Mar 30, 2017

The value of this expression is:

## $\frac{27 {x}^{6}}{64}$

#### Explanation:

${\left(\frac{16}{9 {x}^{4}}\right)}^{- \frac{3}{2}} = {\left(\frac{9 {x}^{4}}{16}\right)}^{\frac{3}{2}} = {\left(\frac{3 {x}^{2}}{4}\right)}^{3} = \frac{27 {x}^{6}}{64}$

In the first step I used the rule that:

## ${a}^{-} b = \frac{1}{a} ^ b$

The second step is :

## ${a}^{\frac{1}{n}} = \sqrt[n]{a}$

Final step is just calculating the cube (third power) of the expression

Mar 30, 2017

color(red)((27x^6)/64

#### Explanation:

${\left(\frac{16}{9 {x}^{4}}\right)}^{-} \left(\frac{3}{2}\right)$

$\therefore = {\left({4}^{2} / \left({3}^{2} {x}^{4}\right)\right)}^{-} \left(\frac{3}{2}\right)$

:.=(4^(2 xx -3/2))/(3^(2 xx -3/2)x^(4 xx -3/2)

$\therefore = \frac{{4}^{- \frac{6}{2}}}{{3}^{- \frac{6}{2}} {x}^{- \frac{12}{2}}}$

$\therefore = \frac{{4}^{-} 3}{{3}^{-} 3 {x}^{-} 6}$

$\therefore = \frac{\frac{1}{4} ^ 3}{\frac{1}{3} ^ 3 \cdot \frac{1}{x} ^ 6}$

$\therefore = \frac{1}{4} ^ 3 \times {3}^{3} / 1 \times {x}^{6} / 1$

:.=color(red)((27x^6)/64