How do you simplify ${(\frac{16}{81})}^{- \frac{3}{4}}$ $(16/81)^(-3/4)$ ?

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Answer 1 · 2016-05-22T09:00:10

$\frac{27}{8}$ $27/8$

$16 = 2^{4}$ $16 = 2^4$ and $81 = 3^{4}$ $81 = 3^4$

${(\frac{2^{4}}{3^{4}})}^{- \frac{3}{4}}$ $((2^4)/(3^4))^(-3/4)$ = ${(\frac{3^{4}}{2^{4}})}^{\frac{3}{4}}$ $((3^4)/(2^4))^(3/4)$

A fraction raised to a negative index can be simplified by using its reciprocal raised to a positive index

${(\frac{3^{4}}{2^{4}})}^{\frac{3}{4}} = {(\frac{3}{2})}^{3} = \frac{27}{8} .$ $(3^4/2^4)^(3/4) = (3/2)^3 = 27/8.$

How do you simplify (1681)−34(16/81)^(-3/4)?