What is 2sqrt(x)*4x^{(-5)/2} ?

The solution to 2sqrt(x)*4x^{(-5)/2} is 8/(x^2)

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simplify 2sqrt(x)*4x^{(-5)/2}

simplify

2 x \cdot 4 x^{\frac{- 5}{2}}

\frac{8}{x ^{2}}

Solution steps

2 x \cdot 4 x^{\frac{- 5}{2}}

Multiply the numbers:

2 \cdot 4 = 8

= 8 x x^{\frac{- 5}{2}}

Apply radical rule:

a = a^{\frac{1}{2}}

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

= 8 x^{\frac{1}{2}} x^{\frac{- 5}{2}}

Apply exponent rule:

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

x^{\frac{1}{2}} x^{\frac{- 5}{2}} = x^{\frac{1}{2} + \frac{- 5}{2}}

= 8 x^{\frac{1}{2} + \frac{- 5}{2}}

\frac{1}{2} + \frac{- 5}{2} = - 2

= 8 x^{- 2}

Apply exponent rule:

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

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

= 8 \cdot \frac{1}{x ^{2}}

Simplify

8 \cdot \frac{1}{x ^{2}} : \frac{8}{x ^{2}}

= \frac{8}{x ^{2}}

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