Question

(256a¹⁶/ 81b⁴) ‐¾

Question from the chapter exponents​

Answer 1

$Given \: \Big( \frac{256a^{16}}{81b^{4}}\Big)^{\frac{-3}{4}}$

$= \Big( \frac{(4a^{4})^{4}}{(3b)^{4}}\Big)^{\frac{-3}{4}}$

$= \Big( \frac{4a^{4}}{3b}\Big)^{4\times \frac{-3}{4}}$

$= \Big( \frac{4a^{4}}{3b}\Big)^{-3}$

$= \Big( \frac{3b}{4a^{4}}\Big)^{3}$

$= \frac{3^{3} b^{3}}{4^{3} (a^{4})^{3}}$

$= \frac{27b^{3}}{64a^{12}}$

Therefore.,

$\red{\Big( \frac{256a^{16}}{81b^{4}}\Big)^{\frac{-3}{4}}}$

$\green {= \frac{27b^{3}}{64a^{12}}}$

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Answer 2

27b³/64a¹²

=> [(4a⁴)⁴/(3b)⁴]-¾

=> [4a⁴/3b]-³

=>3³b³/4³(a⁴)³

=> 27b³/64a¹²

HOPE IT HELPS YOU. PLEASE MARK ME AS A BRAINALIST. I ANSWERED IT WELL KNOW SO PLEASE