What is 1/4 (2x^2+1)^{-1/5}(24x) ?

The solution to 1/4 (2x^2+1)^{-1/5}(24x) is (6x)/((2x^2+1)^{1/5)}

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simplify 1/4 (2x^2+1)^{-1/5}(24x)

simplify

\frac{1}{4} (2 x^{2} + 1)^{- \frac{1}{5}} (24 x)

\frac{6 x}{( 2 x ^{2} + 1 ) ^{\frac{1}{5}}}

Solution steps

\frac{1}{4} (2 x^{2} + 1)^{- \frac{1}{5}} (24 x)

Apply exponent rule:

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

= 24 \cdot \frac{1}{4} \cdot \frac{1}{( 2 x ^{2} + 1 ) ^{\frac{1}{5}}} x

Multiply fractions:

a \cdot \frac{b}{c} \cdot \frac{d}{e} = \frac{a \cdot b \cdot d}{c \cdot e}

= \frac{1 \cdot 1 \cdot 24 x}{4 ( 2 x ^{2} + 1 ) ^{\frac{1}{5}}}

Multiply the numbers:

1 \cdot 1 \cdot 24 = 24

= \frac{24 x}{4 ( 2 x ^{2} + 1 ) ^{\frac{1}{5}}}

Divide the numbers:

\frac{24}{4} = 6

= \frac{6 x}{( 2 x ^{2} + 1 ) ^{\frac{1}{5}}}

e^{x} (e^{- 2 x})

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

\frac{2}{3}^{3}

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

What is 1/4 (2x^2+1)^{-1/5}(24x) ?
The solution to 1/4 (2x^2+1)^{-1/5}(24x) is (6x)/((2x^2+1)^{1/5)}