What is (-144)^{-3/2} ?

The solution to (-144)^{-3/2} is 1/1728 i

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simplify (-144)^{-3/2}

simplify

(- 144)^{- \frac{3}{2}}

\frac{1}{1728} i

Solution steps

(- 144)^{- \frac{3}{2}}

Apply exponent rule:

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

(- 144)^{- \frac{3}{2}} = \frac{1}{( - 144 ) ^{\frac{3}{2}}}

= \frac{1}{( - 144 ) ^{\frac{3}{2}}}

Simplify

\frac{1}{( - 144 ) ^{\frac{3}{2}}} : - \frac{1}{1728 i}

= - \frac{1}{1728 i}

Multiply by the conjugate

\frac{- i}{- i}

= - \frac{1 \cdot ( - i )}{1728 i ( - i )}

Simplify

- \frac{1 \cdot ( - i )}{1728 i ( - i )} : - \frac{- i}{1728}

= - \frac{- i}{1728}

Apply the fraction rule:

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

= \frac{i}{1728}

Rewrite in standard complex form:

\frac{1}{1728} i

= \frac{1}{1728} i

(\frac{2}{3})^{- 5^{^{'}}}

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(6.6726 \cdot 1 0^{- 11}) (3.17 \cdot 1 0^{7})

\frac{( x ^{2} + 1 ) ^{4}}{x ^{4}}

1.57 \cdot 1 0^{- 3} (1 + 5)