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Popular >

simplify (-27/64)^{4/3}

Solution

simplify

(- \frac{27}{64})^{\frac{4}{3}}

Solution

\frac{81}{256}

+1

Solution steps

(- \frac{27}{64})^{\frac{4}{3}}

Apply exponent rule:

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

(- \frac{27}{64})^{\frac{4}{3}} = (- 1)^{\frac{4}{3}} (\frac{27}{64})^{\frac{4}{3}}

= (- 1)^{\frac{4}{3}} (\frac{27}{64})^{\frac{4}{3}}

(- 1)^{\frac{4}{3}} = 1

= 1 \cdot (\frac{27}{64})^{\frac{4}{3}}

Apply exponent rule:

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

(\frac{27}{64})^{\frac{4}{3}} = \frac{2 7 ^{\frac{4}{3}}}{6 4 ^{\frac{4}{3}}}

= 1 \cdot \frac{2 7 ^{\frac{4}{3}}}{6 4 ^{\frac{4}{3}}}

6 4^{\frac{4}{3}} = 256

= 1 \cdot \frac{2 7 ^{\frac{4}{3}}}{256}

2 7^{\frac{4}{3}} = 81

= 1 \cdot \frac{81}{256}

Multiply:

1 \cdot \frac{81}{256} = \frac{81}{256}

= \frac{81}{256}

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Frequently Asked Questions (FAQ)

What is (-27/64)^{4/3} ?
The solution to (-27/64)^{4/3} is 81/256