What is 9x^{3/2}*(3x)^{(-1)/2} ?

The solution to 9x^{3/2}*(3x)^{(-1)/2} is 3^{3/2}x

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simplify 9x^{3/2}*(3x)^{(-1)/2}

simplify

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

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

Solution steps

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

Simplify

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

= 9 x^{\frac{3}{2}} \frac{1}{3 ^{\frac{1}{2}} x ^{\frac{1}{2}}}

Apply the fraction rule:

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

= \frac{9 x ^{\frac{3}{2}} \cdot 1}{3 ^{\frac{1}{2}} x ^{\frac{1}{2}}}

Multiply the numbers:

9 \cdot 1 = 9

= \frac{9 x ^{\frac{3}{2}}}{3 ^{\frac{1}{2}} x ^{\frac{1}{2}}}

Factor the number:

9 = 3^{2}

= \frac{3 ^{2} x ^{\frac{3}{2}}}{3 ^{\frac{1}{2}} x ^{\frac{1}{2}}}

Simplify

\frac{3 ^{2}}{3 ^{\frac{1}{2}}} : 3^{\frac{3}{2}}

= \frac{3 ^{\frac{3}{2}} x ^{\frac{3}{2}}}{x ^{\frac{1}{2}}}

Simplify

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

= 3^{\frac{3}{2}} x

\frac{( 9 + 12 a + 4 a ^{2} )}{( b ^{2} )}

\frac{100}{2 x [ 47 - ( 30 - 2 ^{3} ) ]}

x + (110 - 5 x)

\frac{0}{1 ^{x}}

25 x^{2} - 100 y^{2}

What is 9x^{3/2}*(3x)^{(-1)/2} ?
The solution to 9x^{3/2}*(3x)^{(-1)/2} is 3^{3/2}x