Question

Find the value
5 root (243) raised to power -3​

Answer 1

$Value \:of \:\big( \sqrt[5] 243 \big)^{-3}\\= \big( 243 \big)^{\frac{-3}{5}} \\= \big( 3^{5} \big)^{\frac{-3}{5}} \\= 3^{5 \times \frac{(-3)}{5}}$

$\boxed { \pink { (a^{m})^{n} = a^{m\times n } }}$

$= 3^{-3} \\= \frac{1}{3^{3}}\\= \frac{1}{27}$

Therefore.,

$\red {Value \:of \:\big( \sqrt[5] 243 \big)^{-3}}\green { = \frac{1}{27}}$

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