What is ((8x^9y^3)/(27x^2y^{12)})^{2/3} ?

The solution to ((8x^9y^3)/(27x^2y^{12)})^{2/3} is (4x^{14/3})/(9y^6)

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simplify ((8x^9y^3)/(27x^2y^{12)})^{2/3}

simplify

(\frac{8 x ^{9} y ^{3}}{27 x ^{2} y ^{12}})^{\frac{2}{3}}

\frac{4 x ^{\frac{14}{3}}}{9 y ^{6}}

Solution steps

(\frac{8 x ^{9} y ^{3}}{27 x ^{2} y ^{12}})^{\frac{2}{3}}

Apply exponent rule:

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

= \frac{( 8 x ^{9} y ^{3} ) ^{\frac{2}{3}}}{( 27 x ^{2} y ^{12} ) ^{\frac{2}{3}}}

Simplify

(8 x^{9} y^{3})^{\frac{2}{3}} : 4 x^{6} y^{2}

= \frac{4 x ^{6} y ^{2}}{( 27 x ^{2} y ^{12} ) ^{\frac{2}{3}}}

Simplify

(27 x^{2} y^{12})^{\frac{2}{3}} : 9 x^{\frac{4}{3}} y^{8}

= \frac{4 x ^{6} y ^{2}}{9 x ^{\frac{4}{3}} y ^{8}}

Apply exponent rule:

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

\frac{x ^{6}}{x ^{\frac{4}{3}}} = x^{6 - \frac{4}{3}}

= \frac{4 y ^{2} x ^{- \frac{4}{3} + 6}}{9 y ^{8}}

Subtract the numbers:

6 - \frac{4}{3} = \frac{14}{3}

= \frac{4 y ^{2} x ^{\frac{14}{3}}}{9 y ^{8}}

Apply exponent rule:

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

\frac{y ^{2}}{y ^{8}} = \frac{1}{y ^{8 - 2}}

= \frac{4 x ^{\frac{14}{3}}}{9 y ^{8 - 2}}

Subtract the numbers:

8 - 2 = 6

= \frac{4 x ^{\frac{14}{3}}}{9 y ^{6}}

(x - 8)^{2} - 7 = 25

\frac{x}{3} = - 4

\frac{x}{3} = 2 x + 5

(2 x + 3)^{2}

3 (2 x + 5) \geq 2 (x + 6)

What is ((8x^9y^3)/(27x^2y^{12)})^{2/3} ?
The solution to ((8x^9y^3)/(27x^2y^{12)})^{2/3} is (4x^{14/3})/(9y^6)