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Popular >

simplify \sqrt[3]{(1000)^2}

Solution

simplify

Solution

100

Solution steps

Apply radical rule:

= ((1000)^{2})^{\frac{1}{3}}

Apply exponent rule:

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

= (1000)^{2 \cdot \frac{1}{3}}

2 \cdot \frac{1}{3} = \frac{2}{3}

= (1000)^{\frac{2}{3}}

Factor the number:

1000 = 1 0^{3}

= (1 0^{3})^{\frac{2}{3}}

Apply exponent rule:

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

(1 0^{3})^{\frac{2}{3}} = 1 0^{3 \cdot \frac{2}{3}} = 1 0^{2}

= 1 0^{2}

Refine

= 100

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Frequently Asked Questions (FAQ)

What is \sqrt[3]{(1000)^2} ?
The solution to \sqrt[3]{(1000)^2} is 100