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Popular >

simplify \sqrt[10]{4^x}

Solution

simplify

Solution

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

Solution steps

Apply radical rule:

= (4^{x})^{\frac{1}{10}}

Apply exponent rule:

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

= 4^{x \frac{1}{10}}

Simplify

x \frac{1}{10} : \frac{x}{10}

= 4^{\frac{x}{10}}

Factor the number:

4 = 2^{2}

= (2^{2})^{\frac{x}{10}}

Apply exponent rule:

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

(2^{2})^{\frac{x}{10}} = 2^{2 \cdot \frac{x}{10}} = 2^{\frac{x}{5}}

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

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Frequently Asked Questions (FAQ)

What is \sqrt[10]{4^x} ?
The solution to \sqrt[10]{4^x} is 2^{x/5}