Simplify:$ \sqrt[3]{(343)^{-2}} $

Given:

\( \sqrt[3]{(343)^{-2}} \)

To do:

We have to simplify the given expression.

Solution:

We know that,

$(a^{m})^{n}=a^{m n}$

$a^{m} \times a^{n}=a^{m+n}$

$a^{m} \div a^{n}=a^{m-n}$

$a^{0}=1$

Therefore,

$\sqrt[3]{(343)^{-2}}=(343)^{\frac{-2}{3}}$

$=(7^3)^{\frac{-2}{3}}$

$=(7)^{3\times\frac{-2}{3}}$

$=(7)^{-2}$

$=\frac{1}{7^2}$

$=\frac{1}{49}$

Hence, $\sqrt[3]{(343)^{-2}}=\frac{1}{49}$. 

Tutorialspoint

Updated on: 10-Oct-2022

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