How do you evaluate and simplify $\frac{1}{81^{- (\frac{3}{4})}}$ $1/(81^-(3/4))$ ?

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Answer 1 · 2018-03-22T13:04:09

$\frac{1}{81^{- \frac{3}{4}}} = 27$ $1/81^(-3/4)=27$

We use identities $\frac{1}{a^{- n}} = a^{n}$ $1/a^(-n)=a^n$ and ${(a^{m})}^{n} = a^{m \times n}$ $(a^m)^n=a^(mxxn)$

hence $\frac{1}{81^{- \frac{3}{4}}}$ $1/81^(-3/4)$

= $81^{\frac{3}{4}}$ $81^(3/4)$

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

= $3^{4 \times \frac{3}{4}}$ $3^(4xx3/4)$

= $3^{3}$ $3^3$

= $27$ $27$

How do you evaluate and simplify 1/(81^-(3/4))181−(34)1/(81^-(3/4))?