What is \sqrt[36]{(25/64)^{-18}} ?

The solution to \sqrt[36]{(25/64)^{-18}} is 8/5

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simplify \sqrt[36]{(25/64)^{-18}}

simplify

\frac{8}{5}

Decimal Notation

1.6

Solution steps

Apply radical rule:

= ((\frac{25}{64})^{- 18})^{\frac{1}{36}}

Apply exponent rule:

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

= (\frac{25}{64})^{(- 18) \frac{1}{36}}

(- 18) \frac{1}{36} = - \frac{1}{2}

= (\frac{25}{64})^{- \frac{1}{2}}

Apply exponent rule:

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

= \frac{1}{\frac{25}{64}}

Apply radical rule:

assuming

a \geq 0, b \geq 0

\frac{25}{64} = \frac{25}{64}

= \frac{1}{\frac{25}{64}}

64 = 8

= \frac{1}{\frac{25}{8}}

25 = 5

= \frac{1}{\frac{5}{8}}

Apply the fraction rule:

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

= \frac{8}{5}

(p - q)^{2} \cdot (p + q)^{2}

e^{- 0.221}

e^{\frac{1}{2}} \cdot e^{- \frac{1}{2}}

(1 - x^{2})^{2} x^{2}

What is \sqrt[36]{(25/64)^{-18}} ?
The solution to \sqrt[36]{(25/64)^{-18}} is 8/5