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Popular >

simplify \sqrt[8]{4^3}

Solution

simplify

Solution

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

+1

Decimal Notation

1.68179 \dots

Solution steps

Apply radical rule:

= (4^{3})^{\frac{1}{8}}

Apply exponent rule:

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

= 4^{3 \cdot \frac{1}{8}}

3 \cdot \frac{1}{8} = \frac{3}{8}

= 4^{\frac{3}{8}}

Factor the number:

4 = 2^{2}

= (2^{2})^{\frac{3}{8}}

Apply exponent rule:

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

(2^{2})^{\frac{3}{8}} = 2^{2 \cdot \frac{3}{8}} = 2^{\frac{3}{4}}

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

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Frequently Asked Questions (FAQ)

What is \sqrt[8]{4^3} ?
The solution to \sqrt[8]{4^3} is 2^{3/4}