What is ((6^{1/5})/(6^{2/5)})^3 ?

The solution to ((6^{1/5})/(6^{2/5)})^3 is 1/(6^{3/5)}

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simplify ((6^{1/5})/(6^{2/5)})^3

simplify

(\frac{6 ^{\frac{1}{5}}}{6 ^{\frac{2}{5}}})^{3}

\frac{1}{6 ^{\frac{3}{5}}}

Decimal Notation

0.34127 \dots

Solution steps

(\frac{6 ^{\frac{1}{5}}}{6 ^{\frac{2}{5}}})^{3}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{( 6 ^{\frac{1}{5}} ) ^{3}}{( 6 ^{\frac{2}{5}} ) ^{3}}

(6^{\frac{1}{5}})^{3} = 6^{\frac{3}{5}}

= \frac{6 ^{\frac{3}{5}}}{( 6 ^{\frac{2}{5}} ) ^{3}}

(6^{\frac{2}{5}})^{3} = 6 \cdot 6^{\frac{1}{5}}

= \frac{6 ^{\frac{3}{5}}}{6 \cdot 6 ^{\frac{1}{5}}}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{6 ^{\frac{3}{5}}}{6} = \frac{1}{6 ^{1 - \frac{3}{5}}}

= \frac{1}{6 ^{\frac{1}{5}} \cdot 6 ^{- \frac{3}{5} + 1}}

Subtract the numbers:

1 - \frac{3}{5} = \frac{2}{5}

= \frac{1}{6 ^{\frac{2}{5}} \cdot 6 ^{\frac{1}{5}}}

6^{\frac{2}{5}} \cdot 6^{\frac{1}{5}} = 6^{\frac{2}{5} + \frac{1}{5}}

= \frac{1}{6 ^{\frac{2}{5} + \frac{1}{5}}}

Combine the fractions

\frac{2}{5} + \frac{1}{5} : \frac{3}{5}

= \frac{1}{6 ^{\frac{3}{5}}}

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What is ((6^{1/5})/(6^{2/5)})^3 ?
The solution to ((6^{1/5})/(6^{2/5)})^3 is 1/(6^{3/5)}