What is expand ((5(x^2-1)^3)/(3x))^{1/2} ?

The solution to expand ((5(x^2-1)^3)/(3x))^{1/2} is (5^{1/2}(x^2-1)^{3/2})/(3^{1/2)x^{1/2}}

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expand ((5(x^2-1)^3)/(3x))^{1/2}

expand

(\frac{5 ( x ^{2} - 1 ) ^{3}}{3 x})^{\frac{1}{2}}

\frac{5 ^{\frac{1}{2}} ( x ^{2} - 1 ) ^{\frac{3}{2}}}{3 ^{\frac{1}{2}} x ^{\frac{1}{2}}}

Solution steps

(\frac{5 ( x ^{2} - 1 ) ^{3}}{3 x})^{\frac{1}{2}}

Apply exponent rule:

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

\frac{5 ( x ^{2} - 1 ) ^{3}}{3 x} = \frac{( 5 ( x ^{2} - 1 ) ^{3} ) ^{\frac{1}{2}}}{( 3 x ) ^{\frac{1}{2}}}

= \frac{( 5 ( x ^{2} - 1 ) ^{3} ) ^{\frac{1}{2}}}{( 3 x ) ^{\frac{1}{2}}}

Simplify

(5 (x^{2} - 1)^{3})^{\frac{1}{2}} : 5^{\frac{1}{2}} (x^{2} - 1)^{\frac{3}{2}}

= \frac{5 ^{\frac{1}{2}} ( x ^{2} - 1 ) ^{\frac{3}{2}}}{( 3 x ) ^{\frac{1}{2}}}

Simplify

(3 x)^{\frac{1}{2}} : 3^{\frac{1}{2}} x^{\frac{1}{2}}

= \frac{5 ^{\frac{1}{2}} ( x ^{2} - 1 ) ^{\frac{3}{2}}}{3 ^{\frac{1}{2}} x ^{\frac{1}{2}}}

\frac{( 0.04 + 12 \cdot 1 0 ^{- 2} ) ^{3}}{( 0.02 ) ^{3}}

- e^{- 1} \cdot e^{- 1}

100000 \cdot 0.1 \cdot 1 0^{- 6} \cdot 0.317

π (2)^{2} (2)

What is expand ((5(x^2-1)^3)/(3x))^{1/2} ?
The solution to expand ((5(x^2-1)^3)/(3x))^{1/2} is (5^{1/2}(x^2-1)^{3/2})/(3^{1/2)x^{1/2}}