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Popular >

simplify (\sqrt[4]{9})^3

Solution

simplify

Solution

33

+1

Decimal Notation

5.19615 \dots

Solution steps

Factor the number:

9 = 3^{2}

Apply radical rule:

= ((3^{2})^{\frac{1}{4}})^{3}

Apply exponent rule:

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

= (3^{2})^{\frac{1}{4} \cdot 3}

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

= (3^{2})^{\frac{3}{4}}

Apply exponent rule:

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

= 3^{2 \cdot \frac{3}{4}}

2 \cdot \frac{3}{4} = \frac{3}{2}

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

3^{\frac{3}{2}} = 33

= 33

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Frequently Asked Questions (FAQ)

What is (\sqrt[4]{9})^3 ?
The solution to (\sqrt[4]{9})^3 is 3sqrt(3)