What is ((16x^5y^{10})/(81xy^2))^{3/4} ?

The solution to ((16x^5y^{10})/(81xy^2))^{3/4} is (8x^3y^6)/(27)

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simplify ((16x^5y^{10})/(81xy^2))^{3/4}

simplify

(\frac{16 x ^{5} y ^{10}}{81 x y ^{2}})^{\frac{3}{4}}

\frac{8 x ^{3} y ^{6}}{27}

Solution steps

(\frac{16 x ^{5} y ^{10}}{81 x y ^{2}})^{\frac{3}{4}}

Apply exponent rule:

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

= \frac{( 16 x ^{5} y ^{10} ) ^{\frac{3}{4}}}{( 81 x y ^{2} ) ^{\frac{3}{4}}}

Simplify

(16 x^{5} y^{10})^{\frac{3}{4}} : 8 x^{\frac{15}{4}} y^{\frac{15}{2}}

= \frac{8 x ^{\frac{15}{4}} y ^{\frac{15}{2}}}{( 81 x y ^{2} ) ^{\frac{3}{4}}}

Simplify

(81 x y^{2})^{\frac{3}{4}} : 27 x^{\frac{3}{4}} y^{\frac{3}{2}}

= \frac{8 x ^{\frac{15}{4}} y ^{\frac{15}{2}}}{27 x ^{\frac{3}{4}} y ^{\frac{3}{2}}}

Apply exponent rule:

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

\frac{x ^{\frac{15}{4}}}{x ^{\frac{3}{4}}} = x^{\frac{15}{4} - \frac{3}{4}}

= \frac{8 y ^{\frac{15}{2}} x ^{\frac{15}{4} - \frac{3}{4}}}{27 y ^{\frac{3}{2}}}

Subtract the numbers:

\frac{15}{4} - \frac{3}{4} = 3

= \frac{8 x ^{3} y ^{\frac{15}{2}}}{27 y ^{\frac{3}{2}}}

Apply exponent rule:

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

\frac{y ^{\frac{15}{2}}}{y ^{\frac{3}{2}}} = y^{\frac{15}{2} - \frac{3}{2}}

= \frac{8 x ^{3} y ^{\frac{15}{2} - \frac{3}{2}}}{27}

Subtract the numbers:

\frac{15}{2} - \frac{3}{2} = 6

= \frac{8 x ^{3} y ^{6}}{27}

lo g_{5} (25) = 3 x + 1

x^{3} - 4 x^{2} - 25 x + 100

5 x - 20 \geq 0

x + 8 \geq 10

x^{2} - 5 x + 16 = 0

What is ((16x^5y^{10})/(81xy^2))^{3/4} ?
The solution to ((16x^5y^{10})/(81xy^2))^{3/4} is (8x^3y^6)/(27)