Question

simplify and express with positive index (3^-4/2^-8)^1/4​

Answer 1

$\Big( \frac{3^{-4}}{2^{-8}}\Big)^{\frac{1}{4}}\\= \Big( \frac{2^{8}}{3^{4}}\Big)^{\frac{1}{4}}$

$\boxed { \pink { Since,a^{-n} = \frac{1}{a^{n}} }}$

$= \Big( \frac{(2^{2})^{4}}{3^{4}}\Big)^{\frac{1}{4}} \\= \Big(\big( \frac{2^{2}}{3}\big)^{4}\Big)^{\frac{1}{4}}\\= \Big(\frac{4}{3}\Big)^{4\times \frac{1}{4}} \\= \frac{4}{3}$

Therefore.,

$\red{\Big( \frac{3^{-4}}{2^{-8}}\Big)^{\frac{1}{4}}}$

$\green { = \frac{4}{3} }$

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