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

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

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

simplify

Solution steps

Apply radical rule:

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

Apply exponent rule:

(a^{b})^{c} = a^{b c},

assuming

a \geq 0

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

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

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

Apply exponent rule:

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

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

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

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

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

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

Combine same powers :

10 \cdot 6.023 \cdot 1 0^{23}

e^{- 3 t} f (t - 1)

1 0^{3} \cdot (4.7 \cdot 1 0^{- 6})

4.5 (4.5)^{2} (0.0004)

62 x x

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