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Exponents Of Real Numbers — Maths STD 9 — Question

Maharashtra BoardEnglish MediumSTD 9MathsExponents Of Real Numbers2 Marks
Question
Simplify:$\sqrt[3]{(343)^{-2}}$
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Answer

We have,$\sqrt[3]{(343)^{-2}}=\sqrt[3]{\frac{1}{(343)^2}}$
$=\frac{1}{(343)^{\frac{2}{3}}}$
$=\frac{1}{(7^3)^{\frac{2}{3}}}$
$=\frac{1}{7^{3\times\frac{2}{3}}}$
$=\frac{1}{7^2}$
$=\frac{1}{49}$
$\Rightarrow\sqrt[3]{(343)^{-2}}=\frac{1}{49}$

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