Question

Solve [(5/6)^1/5]^-1/6

Answer 1

Hello Mate here is your answer below,,

$(( \frac{5}{6} ) {}^{ \frac{1}{5} } ) {}^ { - \frac{1}{6} } \\ ( \frac{5}{6} ) {}^{ \frac{1}{5} \times( - \frac{1}{6})} \\ (\frac{5}{6}){}^{ \frac{1}{5} \times - \frac{1}{6} } \\ ( \frac{5}{6} ) {}^{ - \frac{1}{30} }$

I hope that helps you

Answer 2

The simplified expression is  $(\dfrac{6}{5})^{\dfrac{1}{30}}$.

Explanation:

The expression : $[(\dfrac{5}{6})^{\dfrac{1}{5}}]^{\dfrac{-1}{6}}$

Using exponential identity :

$(a^m)^n = a^{mn}$

Then,

$[(\dfrac{5}{6})^{\dfrac{1}{5}}]^{\dfrac{-1}{6}}=[(\dfrac{5}{6})^{\dfrac{1}{5}\times\dfrac{-1}{6}}]\\\\=(\dfrac{5}{6})^{\dfrac{-1}{30}}$

Also, $a^{-n}=\dfrac{1}{a}$

Therefore , $(\dfrac{5}{6})^{\dfrac{-1}{30}}=(\dfrac{6}{5})^{\dfrac{1}{30}}$

Hence, the simplified expression is  $(\dfrac{6}{5})^{\dfrac{1}{30}}$.

# Learn more :

Solve the equation.

x + 1/6 = 6

A.x = –6 1/6

B.x = –5 5/6

C.x = 5 5/6

D.x = 6 1/6

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