How do you simplify ${(5 a)}^{- 2}$ $(5a)^-2$ ?

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How do you simplify ${(5 a)}^{- 2}$ $(5a)^-2$ ?

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Answer 1 · 2017-07-24T09:55:31

$\frac{1}{25 a^{2}}$ $1/(25a^2)$

Explanation:

$using the laws of exponents$ $"using the "color(blue)"laws of exponents"$

$∙ x {(a b)}^{n} = a^{n} b^{n}$ $•color(white)(x)(ab)^n=a^nb^n$

$∙ x a^{- n} \Leftrightarrow \frac{1}{a^{n}}$ $•color(white)(x)a^-nhArr1/a^n$

$\Rightarrow {(5 a)}^{- 2}$ $rArr(5a)^-2$

$= 5^{- 2} \times a^{- 2}$ $=5^-2xxa^-2$

$= \frac{1}{5^{2}} \times \frac{1}{a^{2}} = \frac{1}{25} \times \frac{1}{a^{2}} = \frac{1}{25 a^{2}}$ $=1/5^2xx1/a^2=1/25xx1/a^2=1/(25a^2)$

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How do you simplify ${(5 a)}^{- 2}$ $(5a)^-2$ ?

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