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Popular >

simplify \sqrt[4]{(3x)^3}

Solution

simplify

Solution

3^{\frac{3}{4}} x^{\frac{3}{4}}

Solution steps

Apply radical rule:

= ((3 x)^{3})^{\frac{1}{4}}

Apply exponent rule:

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

assuming

a \geq 0

= (3 x)^{3 \cdot \frac{1}{4}}

3 \cdot \frac{1}{4} = \frac{3}{4}

= (3 x)^{\frac{3}{4}}

Apply exponent rule:

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

= 3^{\frac{3}{4}} x^{\frac{3}{4}}

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Frequently Asked Questions (FAQ)

What is \sqrt[4]{(3x)^3} ?
The solution to \sqrt[4]{(3x)^3} is 3^{3/4}x^{3/4}