What is \sqrt[3]{((-1)/(27))}^5 ?

The solution to \sqrt[3]{((-1)/(27))}^5 is -(\sqrt[3]{(-1)^2})/(243)

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simplify \sqrt[3]{((-1)/(27))}^5

simplify

Solution steps

Apply rule:

(a) = a

(\frac{- 1}{27}) = \frac{- 1}{27}

Apply exponent rule:

a^{b + c} = a^{b} \cdot a^{c}

Apply exponent rule:

Apply radical rule:

= \frac{- 1}{27} ((\frac{- 1}{27})^{\frac{1}{3}})^{2}

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

((\frac{- 1}{27})^{\frac{1}{3}})^{2} = (\frac{- 1}{27})^{\frac{1}{3} \cdot 2}

= \frac{- 1}{27} (\frac{- 1}{27})^{\frac{1}{3} \cdot 2}

\frac{1}{3} \cdot 2 = \frac{2}{3}

= \frac{- 1}{27} (\frac{- 1}{27})^{\frac{2}{3}}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

\frac{- 1}{27} (\frac{- 1}{27})^{\frac{2}{3}} = (\frac{- 1}{27})^{1 + \frac{2}{3}}

= (\frac{- 1}{27})^{1 + \frac{2}{3}}

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

= (\frac{- 1}{27})^{\frac{5}{3}}

Apply exponent rule:

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

= \frac{( - 1 ) ^{\frac{5}{3}}}{2 7 ^{\frac{5}{3}}}

2 7^{\frac{5}{3}} = 243

= \frac{( - 1 ) ^{\frac{5}{3}}}{243}

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

= \frac{- ( - 1 ) ^{\frac{2}{3}}}{243}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{( - 1 ) ^{\frac{2}{3}}}{243}

(π \cdot 5 \cdot 10) \cdot (π \cdot 5^{2})

(7 w^{2}) (4 w^{2})

What is \sqrt[3]{((-1)/(27))}^5 ?
The solution to \sqrt[3]{((-1)/(27))}^5 is -(\sqrt[3]{(-1)^2})/(243)