How to simplify this?

Question

How to simplify this?

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

2 Answers

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Answer 1 · 2017-03-30T07:17:07

The value of this expression is:

$\frac{27 x^{6}}{64}$ $(27x^6)/64$

Explanation:

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

In the first step I used the rule that:

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

The second step is :

$a^{\frac{1}{n}} = \sqrt[n]{a}$ $a^(1/n)=root(n)(a)$

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

Answer 2 · 2017-03-30T08:54:36

$\frac{27 x^{6}}{64}$ $color(red)((27x^6)/64$

Explanation:

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

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

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

$:.=(4^(-6/2))/(3^(-6/2)x^(-12/2))$

$:.=(4^-3)/(3^-3 x^-6)$

$:.=(1/4^3)/(1/3^3*1/x^6)$

$:.=1/4^3 xx 3^3/1 xx x^6/1$

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

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How to simplify this?

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

2 Answers

$\frac{27 x^{6}}{64}$ $(27x^6)/64$

Explanation:

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

$a^{\frac{1}{n}} = \sqrt[n]{a}$ $a^(1/n)=root(n)(a)$

Explanation:

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How to simplify this?

(16/(9x^4))^(-(3/2))(169x4)−(32)(16/(9x^4))^(-(3/2))

2 Answers

(27x^6)/6427x664(27x^6)/64

Explanation:

a^-b=1/a^ba−b=1aba^-b=1/a^b

a^(1/n)=root(n)(a)a1n=n√aa^(1/n)=root(n)(a)

Explanation:

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Impact of this question

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

$\frac{27 x^{6}}{64}$ $(27x^6)/64$

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

$a^{\frac{1}{n}} = \sqrt[n]{a}$ $a^(1/n)=root(n)(a)$