What is ((9st)^{3/2})/((27s^3t^{-4))^{2/3}} ?

The solution to ((9st)^{3/2})/((27s^3t^{-4))^{2/3}} is (3t^{25/6})/(s^{1/2)}

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simplify ((9st)^{3/2})/((27s^3t^{-4))^{2/3}}

simplify

\frac{( 9 s t ) ^{\frac{3}{2}}}{( 27 s ^{3} t ^{- 4} ) ^{\frac{2}{3}}}

\frac{3 t ^{\frac{25}{6}}}{s ^{\frac{1}{2}}}

Solution steps

\frac{( 9 s t ) ^{\frac{3}{2}}}{( 27 s ^{3} t ^{- 4} ) ^{\frac{2}{3}}}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(9 s t)^{\frac{3}{2}} = 9^{\frac{3}{2}} s^{\frac{3}{2}} t^{\frac{3}{2}}

= \frac{9 ^{\frac{3}{2}} s ^{\frac{3}{2}} t ^{\frac{3}{2}}}{( 27 s ^{3} t ^{- 4} ) ^{\frac{2}{3}}}

Simplify

(27 s^{3} t^{- 4})^{\frac{2}{3}} : 2 7^{\frac{2}{3}} s^{2} \frac{1}{t ^{\frac{8}{3}}}

= \frac{9 ^{\frac{3}{2}} s ^{\frac{3}{2}} t ^{\frac{3}{2}}}{2 7 ^{\frac{2}{3}} s ^{2} \frac{1}{t ^{\frac{8}{3}}}}

Factor

2 7^{\frac{2}{3}} : 9^{\frac{2}{3}} \cdot 3^{\frac{2}{3}}

= \frac{9 ^{\frac{3}{2}} s ^{\frac{3}{2}} t ^{\frac{3}{2}}}{9 ^{\frac{2}{3}} \cdot 3 ^{\frac{2}{3}} s ^{2} \frac{1}{t ^{\frac{8}{3}}}}

Simplify

\frac{9 ^{\frac{3}{2}}}{9 ^{\frac{2}{3}}} : 9^{\frac{5}{6}}

= \frac{9 ^{\frac{5}{6}} s ^{\frac{3}{2}} t ^{\frac{3}{2}}}{3 ^{\frac{2}{3}} s ^{2} \frac{1}{t ^{\frac{8}{3}}}}

Factor

9^{\frac{5}{6}} : 3^{\frac{5}{3}}

= \frac{3 ^{\frac{5}{3}} s ^{\frac{3}{2}} t ^{\frac{3}{2}}}{3 ^{\frac{2}{3}} s ^{2} \frac{1}{t ^{\frac{8}{3}}}}

Simplify

\frac{3 ^{\frac{5}{3}}}{3 ^{\frac{2}{3}}} : 3

= \frac{3 s ^{\frac{3}{2}} t ^{\frac{3}{2}}}{s ^{2} \frac{1}{t ^{\frac{8}{3}}}}

Simplify

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

= \frac{3 t ^{\frac{3}{2}}}{s ^{\frac{1}{2}} \frac{1}{t ^{\frac{8}{3}}}}

Simplify

\frac{3 t ^{\frac{3}{2}}}{s ^{\frac{1}{2}} \frac{1}{t ^{\frac{8}{3}}}} : \frac{3 t ^{\frac{25}{6}}}{s ^{\frac{1}{2}}}

= \frac{3 t ^{\frac{25}{6}}}{s ^{\frac{1}{2}}}

x - 12 + 4 x = - 2 x - 28 + x

2 x^{2} + 7 x + 15 = 0

\frac{1}{16} \cdot 3

7 x + 15 = 1

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

What is ((9st)^{3/2})/((27s^3t^{-4))^{2/3}} ?
The solution to ((9st)^{3/2})/((27s^3t^{-4))^{2/3}} is (3t^{25/6})/(s^{1/2)}