 # Rewrite the following exponential expressions as equivalent radical expressions. If topoit8d 2022-05-02 Answered
Rewrite the following exponential expressions as equivalent radical expressions. If the number is rational, write it without radicals or exponents.
${27}^{-\frac{2}{3}}$
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Given: ${27}^{-\frac{2}{3}}$
Process $\frac{1}{{27}^{\frac{2}{3}}}$
$\frac{1}{\sqrt{{27}^{2}}}$
$27={3}^{3}$
$=\frac{1}{\sqrt{{3}^{32}}}$
$=\frac{1}{\sqrt{{3}^{6}}}$
$=\frac{1}{{3}^{\frac{6}{3}}}$
$=\frac{1}{9}$

###### Not exactly what you’re looking for? dagars5nx
Step-by-step explanation:
Simplify:
${27}^{-\frac{2}{3}}$
$={\frac{1}{27}}^{\frac{2}{3}}$
$=\frac{1}{{\left[{27}^{\frac{1}{3}}\right]}^{2}}$
$={\frac{1}{{\left[3×3×3\right]}^{\frac{1}{3}}}}^{2}$
$={\frac{1}{3}}^{2}$
$=\frac{1}{9}$