What is ((-27/8)^{-2/3})^{1/2} ?

The solution to ((-27/8)^{-2/3})^{1/2} is -2/3

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simplify ((-27/8)^{-2/3})^{1/2}

simplify

((- \frac{27}{8})^{- \frac{2}{3}})^{\frac{1}{2}}

- \frac{2}{3}

Decimal Notation

- 0.66666 \dots

Solution steps

((- \frac{27}{8})^{- \frac{2}{3}})^{\frac{1}{2}}

Apply exponent rule:

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

= (- \frac{27}{8})^{(- \frac{2}{3}) \frac{1}{2}}

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

= (- \frac{27}{8})^{- \frac{1}{3}}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

= \frac{1}{( - \frac{27}{8} ) ^{\frac{1}{3}}}

Apply exponent rule:

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

n

is odd

(- \frac{27}{8})^{\frac{1}{3}} = - (\frac{27}{8})^{\frac{1}{3}}

= \frac{1}{- ( \frac{27}{8} ) ^{\frac{1}{3}}}

Apply radical rule:

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

assuming

a \geq 0, b \geq 0

(\frac{27}{8})^{\frac{1}{3}} = \frac{2 7 ^{\frac{1}{3}}}{8 ^{\frac{1}{3}}}

= \frac{1}{- \frac{2 7 ^{\frac{1}{3}}}{8 ^{\frac{1}{3}}}}

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

= \frac{1}{- \frac{2 7 ^{\frac{1}{3}}}{2}}

2 7^{\frac{1}{3}} = 3

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

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

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

Apply the fraction rule:

\frac{1}{\frac{b}{c}} = \frac{c}{b}

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

= - \frac{2}{3}

1.36 \cdot 1 0^{- 3}

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(4 e^{- 3 j})^{- 2}