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Popular >

simplify (8^2)^{1/3}

Solution

simplify

(8^{2})^{\frac{1}{3}}

Solution

4

Solution steps

(8^{2})^{\frac{1}{3}}

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

= 8^{2 \cdot \frac{1}{3}}

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

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

Factor the number:

8 = 2^{3}

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

Apply exponent rule:

(a^{b})^{c} = a^{b c}, a \geq 0

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

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

= 2^{2}

2^{2} = 4

= 4

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Frequently Asked Questions (FAQ)

What is (8^2)^{1/3} ?
The solution to (8^2)^{1/3} is 4