What is a{(24a^4*b^3)/((sqrt(2a^2*b)))}^{3/2} ?

The solution to a{(24a^4*b^3)/((sqrt(2a^2*b)))}^{3/2} is 2^{3/4}*3^{1/2}*24a^{11/2}b^{15/4}

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simplify a{(24a^4b^3)/((sqrt(2a^2b)))}^{3/2}

simplify

a ⎩ ⎨ ⎧ \frac{24 a ^{4} \cdot b ^{3}}{( 2 a ^{2} \cdot b )} ⎭ ⎬ ⎫^{\frac{3}{2}}

2^{\frac{3}{4}} \cdot 3^{\frac{1}{2}} \cdot 24 a^{\frac{11}{2}} b^{\frac{15}{4}}

Solution steps

a (\frac{24 a ^{4} b ^{3}}{2 a ^{2} b})^{\frac{3}{2}}

Simplify

(\frac{24 a ^{4} b ^{3}}{2 a ^{2} b})^{\frac{3}{2}} : 24 \cdot 2^{\frac{3}{4}} \cdot 3^{\frac{1}{2}} a^{\frac{9}{2}} b^{\frac{15}{4}}

= a \cdot 24 \cdot 2^{\frac{3}{4}} \cdot 3^{\frac{1}{2}} a^{\frac{9}{2}} b^{\frac{15}{4}}

Simplify

a a^{\frac{9}{2}} : a^{\frac{11}{2}}

= a^{\frac{11}{2}} \cdot 24 \cdot 2^{\frac{3}{4}} \cdot 3^{\frac{1}{2}} b^{\frac{15}{4}}

= 2^{\frac{3}{4}} \cdot 3^{\frac{1}{2}} \cdot 24 a^{\frac{11}{2}} b^{\frac{15}{4}}

\frac{( 20 x ^{3} + 40 x ^{5} )}{( 5 x ^{2} + 4 x ^{3} )}

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\frac{( 33.3 \cdot 1 0 ^{- 3} - x )}{( ( x ) ( x ) )}

5.1 (1 - x)^{2}

a^{2} - 1 - 2 x - x^{2}

What is a{(24a^4*b^3)/((sqrt(2a^2*b)))}^{3/2} ?
The solution to a{(24a^4*b^3)/((sqrt(2a^2*b)))}^{3/2} is 2^{3/4}*3^{1/2}*24a^{11/2}b^{15/4}