What is (-2x^3)(2x^{-5}) ?

The solution to (-2x^3)(2x^{-5}) is -4/(x^2)

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simplify (-2x^3)(2x^{-5})

simplify

(- 2 x^{3}) (2 x^{- 5})

- \frac{4}{x ^{2}}

Solution steps

(- 2 x^{3}) (2 x^{- 5})

Apply rule:

(- a) = - a

(- 2 x^{3}) = - 2 x^{3}

= - 2 x^{3} \cdot 2 x^{- 5}

Multiply the numbers:

- 2 \cdot 2 = - 4

= - 4 x^{3} x^{- 5}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

x^{3} x^{- 5} = x^{3 - 5}

= - 4 x^{3 - 5}

Subtract the numbers:

3 - 5 = - 2

= - 4 x^{- 2}

Apply exponent rule:

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

x^{- 2} = \frac{1}{x ^{2}}

= - 4 \cdot \frac{1}{x ^{2}}

Simplify

- 4 \cdot \frac{1}{x ^{2}} : - \frac{4}{x ^{2}}

= - \frac{4}{x ^{2}}

\frac{150}{30}

(1 - \frac{1}{x})^{2}

\frac{1}{2} \cdot 60

ln (x^{2} - 7)

\frac{( 1 - i ) ( 2 - i )}{1 - 2 i}