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Popular >

simplify (\sqrt[5]{-1/3})^{15}

Solution

simplify

Solution

- \frac{1}{27}

+1

Decimal Notation

- 0.03703 \dots

Solution steps

Rewrite

15

as

5 \cdot 3

Apply exponent rule:

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

Apply exponent rule:

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

Apply exponent rule:

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

if

n

is odd

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

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

Apply exponent rule:

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

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

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

1^{3} = 1

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

3^{3} = 27

= - \frac{1}{27}

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Frequently Asked Questions (FAQ)

What is (\sqrt[5]{-1/3})^{15} ?
The solution to (\sqrt[5]{-1/3})^{15} is -1/27