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Popular >

simplify \sqrt[5]{1024^3}

Solution

simplify

Solution

64

Solution steps

Apply radical rule:

= (102 4^{3})^{\frac{1}{5}}

Apply exponent rule:

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

= 102 4^{3 \cdot \frac{1}{5}}

3 \cdot \frac{1}{5} = \frac{3}{5}

= 102 4^{\frac{3}{5}}

Factor the number:

1024 = 4^{5}

= (4^{5})^{\frac{3}{5}}

Apply exponent rule:

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

(4^{5})^{\frac{3}{5}} = 4^{5 \cdot \frac{3}{5}} = 4^{3}

= 4^{3}

Refine

= 64

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Frequently Asked Questions (FAQ)

What is \sqrt[5]{1024^3} ?
The solution to \sqrt[5]{1024^3} is 64