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Popular >

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

Solution

simplify

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

Solution

\frac{1}{4}

+1

Solution steps

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

Apply exponent rule:

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

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

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

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

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

Apply exponent rule:

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

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

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

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

= 1 \cdot \frac{1 ^{\frac{2}{3}}}{4}

Multiply:

1 \cdot \frac{1 ^{\frac{2}{3}}}{4} = \frac{1 ^{\frac{2}{3}}}{4}

= \frac{1 ^{\frac{2}{3}}}{4}

Apply rule

1^{a} = 1

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

= \frac{1}{4}

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Frequently Asked Questions (FAQ)

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