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Popular >

simplify (\sqrt[3]{e^2})^{ln(125)}

Solution

simplify

Solution

25

Solution steps

= (e^{\frac{2}{3}})^{l n (125)}

Apply exponent rule:

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

= e^{\frac{2}{3} l n (125)}

\frac{2}{3} ln (125) = 2 ln (5)

= e^{2 l n (5)}

Apply exponent rule:

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

= (e^{l n (5)})^{2}

Apply log rule:

a^{l o g_{a} (b)} = b

e^{l n (5)} = 5

= 5^{2}

5^{2} = 25

= 25

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Frequently Asked Questions (FAQ)

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