What is (\sqrt[3]{(125)/(2pi)})^2 ?

The solution to (\sqrt[3]{(125)/(2pi)})^2 is (25)/(2^{2/3)pi^{2/3}}

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simplify (\sqrt[3]{(125)/(2pi)})^2

simplify

\frac{25}{2 ^{\frac{2}{3}} π ^{\frac{2}{3}}}

Decimal Notation

7.34209 \dots

Solution steps

Apply radical rule:

= ((\frac{125}{2 π})^{\frac{1}{3}})^{2}

Apply exponent rule:

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

= (\frac{125}{2 π})^{\frac{1}{3} \cdot 2}

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

= (\frac{125}{2 π})^{\frac{2}{3}}

Apply exponent rule:

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

= \frac{12 5 ^{\frac{2}{3}}}{( 2 π ) ^{\frac{2}{3}}}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(2 π)^{\frac{2}{3}} = 2^{\frac{2}{3}} π^{\frac{2}{3}}

= \frac{12 5 ^{\frac{2}{3}}}{2 ^{\frac{2}{3}} π ^{\frac{2}{3}}}

12 5^{\frac{2}{3}} = 25

= \frac{25}{2 ^{\frac{2}{3}} π ^{\frac{2}{3}}}

x + 11 \cdot 11

e^{- 2 x} x d x

I n (1.62 \cdot 1 0^{- 1})

What is (\sqrt[3]{(125)/(2pi)})^2 ?
The solution to (\sqrt[3]{(125)/(2pi)})^2 is (25)/(2^{2/3)pi^{2/3}}