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Popular >

simplify \sqrt[60]{125^{40}}

Solution

simplify

Solution

25

Solution steps

Apply radical rule:

= (12 5^{40})^{\frac{1}{60}}

Apply exponent rule:

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

= 12 5^{40 \cdot \frac{1}{60}}

40 \cdot \frac{1}{60} = \frac{2}{3}

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

Factor the number:

125 = 5^{3}

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

Apply exponent rule:

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

(5^{3})^{\frac{2}{3}} = 5^{3 \cdot \frac{2}{3}} = 5^{2}

= 5^{2}

Refine

= 25

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Frequently Asked Questions (FAQ)

What is \sqrt[60]{125^{40}} ?
The solution to \sqrt[60]{125^{40}} is 25