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Popular >

simplify \sqrt[5]{(5x)^2}

Solution

simplify

Solution

5^{\frac{2}{5}} x^{\frac{2}{5}}

Solution steps

Apply radical rule:

= ((5 x)^{2})^{\frac{1}{5}}

Apply exponent rule:

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

assuming

a \geq 0

= (5 x)^{2 \cdot \frac{1}{5}}

2 \cdot \frac{1}{5} = \frac{2}{5}

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

Apply exponent rule:

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

= 5^{\frac{2}{5}} x^{\frac{2}{5}}

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Frequently Asked Questions (FAQ)

What is \sqrt[5]{(5x)^2} ?
The solution to \sqrt[5]{(5x)^2} is 5^{2/5}x^{2/5}