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Popular >

simplify \sqrt[3]{125^{5x+1}}

Solution

simplify

Solution

5^{5 x + 1}

Solution steps

Apply radical rule:

= (12 5^{5 x + 1})^{\frac{1}{3}}

Apply exponent rule:

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

= 12 5^{(5 x + 1) \frac{1}{3}}

Simplify

(5 x + 1) \frac{1}{3} : \frac{5 x + 1}{3}

= 12 5^{\frac{5 x + 1}{3}}

Factor the number:

125 = 5^{3}

= (5^{3})^{\frac{5 x + 1}{3}}

Apply exponent rule:

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

(5^{3})^{\frac{5 x + 1}{3}} = 5^{3 \cdot \frac{5 x + 1}{3}} = 5^{5 x + 1}

= 5^{5 x + 1}

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Frequently Asked Questions (FAQ)

What is \sqrt[3]{125^{5x+1}} ?
The solution to \sqrt[3]{125^{5x+1}} is 5^{5x+1}