What is ((3x^2y^6)/(6xy^2))^3 ?

The solution to ((3x^2y^6)/(6xy^2))^3 is (x^3y^{12})/8

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simplify ((3x^2y^6)/(6xy^2))^3

simplify

(\frac{3 x ^{2} y ^{6}}{6 x y ^{2}})^{3}

\frac{x ^{3} y ^{12}}{8}

Solution steps

(\frac{3 x ^{2} y ^{6}}{6 x y ^{2}})^{3}

Apply exponent rule:

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

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

Simplify

(3 x^{2} y^{6})^{3} : 27 x^{6} y^{18}

= \frac{27 x ^{6} y ^{18}}{( 6 x y ^{2} ) ^{3}}

Simplify

(6 x y^{2})^{3} : 216 x^{3} y^{6}

= \frac{27 x ^{6} y ^{18}}{216 x ^{3} y ^{6}}

Cancel the common factor:

27

= \frac{x ^{6} y ^{18}}{8 x ^{3} y ^{6}}

Apply exponent rule:

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

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

= \frac{y ^{18} x ^{6 - 3}}{8 y ^{6}}

Subtract the numbers:

6 - 3 = 3

= \frac{x ^{3} y ^{18}}{8 y ^{6}}

Apply exponent rule:

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

\frac{y ^{18}}{y ^{6}} = y^{18 - 6}

= \frac{x ^{3} y ^{18 - 6}}{8}

Subtract the numbers:

18 - 6 = 12

= \frac{x ^{3} y ^{12}}{8}

54 - 24 + 150

x^{4} - x^{5}

\frac{20 a ^{2}}{81 b ^{2}}

lo g_{30} (1)

\frac{2}{3 - 5}

What is ((3x^2y^6)/(6xy^2))^3 ?
The solution to ((3x^2y^6)/(6xy^2))^3 is (x^3y^{12})/8