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Popular >

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

Solution

simplify

Solution

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

+1

Solution steps

Apply radical rule:

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

Apply exponent rule:

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

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

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

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

Apply exponent rule:

(- a)^{\frac{m}{n}} = (- 1)^{\frac{m}{n}} (a)^{\frac{m}{n}}

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

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

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

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

Multiply:

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

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

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Frequently Asked Questions (FAQ)

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