Find the value of $216^{- \frac{1}{15}}$ $216^(-1/15)$ ?

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Answer 1 · 2017-06-07T13:34:57

$216^{- \frac{1}{15}} = \frac{1}{\sqrt[5]{6}}$ $216^(-1/15)=1/root(5)6$

As $216 = 2 \times 2 \times 2 \times 3 \times 3 \times 3 = 2^{3} \times 3^{3}$ $216=2xx2xx2xx3xx3xx3=2^3xx3^3$

$216^{- \frac{1}{15}}$ $216^(-1/15)$

= ${(2^{3} \times 3^{3})}^{- \frac{1}{15}}$ $(2^3xx3^3)^(-1/15)$

= ${(2^{3})}^{- \frac{1}{15}} \times {(3^{3})}^{- \frac{1}{15}}$ $(2^3)^(-1/15)xx(3^3)^(-1/15)$

= $2^{(3 \times \frac{- 1}{15})} \times 3^{(3 \times \frac{- 1}{15})}$ $2^((3xx(-1)/15))xx3^((3xx(-1)/15)$

= $2^{- \frac{1}{5}} \times 3^{- \frac{1}{5}}$ $2^(-1/5)xx3^(-1/5)$

= $\frac{1}{2^{\frac{1}{5}}} \times \frac{1}{3^{\frac{1}{5}}}$ $1/2^(1/5)xx1/3^(1/5)$

= $\frac{1}{6^{\frac{1}{5}}}$ $1/6^(1/5)$

= $\frac{1}{\sqrt[5]{6}}$ $1/root(5)6$

Answer 2 · 2018-06-10T18:25:15

$\frac{1}{\sqrt[5]{6}}$ $1/(root(5)6)$

${(216)}^{- \frac{1}{15}}$ $(216)^(-1/15)$

$:.=(6^3)^(-1/15)$

$:.=6^(-3/15)$

$:.=6^(-1/5)$

$:.=1/(6^(1/5))$

$:.=1/(root(5)6)$

Find the value of 216^(-1/15)216−115216^(-1/15)?