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Popular >

simplify (\sqrt[4]{(-2)^3})^8

Solution

simplify

Solution

64

Solution steps

= ((- 2)^{\frac{3}{4}})^{8}

(- 2)^{\frac{3}{4}} = (- 1)^{\frac{3}{4}} \cdot 2^{\frac{3}{4}}

= ((- 1)^{\frac{3}{4}} \cdot 2^{\frac{3}{4}})^{8}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

= (2^{\frac{3}{4}})^{8} ((- 1)^{\frac{3}{4}})^{8}

((- 1)^{\frac{3}{4}})^{8} : (- 1)^{6}

= (- 1)^{6} (2^{\frac{3}{4}})^{8}

Apply exponent rule:

(- a)^{n} = a^{n},

if

n

is even

(- 1)^{6} = 1^{6}

= 1^{6} (2^{\frac{3}{4}})^{8}

(2^{\frac{3}{4}})^{8} : 2^{6}

= 1^{6} \cdot 2^{6}

Apply rule

1^{a} = 1

1^{6} = 1

= 2^{6} \cdot 1

Multiply:

1 \cdot 2^{6} = 2^{6}

= 2^{6}

2^{6} = 64

= 64

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Frequently Asked Questions (FAQ)

What is (\sqrt[4]{(-2)^3})^8 ?
The solution to (\sqrt[4]{(-2)^3})^8 is 64