What is ((4x^5y)/(16xy^4))^3 ?

The solution to ((4x^5y)/(16xy^4))^3 is (x^{12})/(64y^9)

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simplify ((4x^5y)/(16xy^4))^3

simplify

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

\frac{x ^{12}}{64 y ^{9}}

Solution steps

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

Apply exponent rule:

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

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

Simplify

(4 x^{5} y)^{3} : 64 x^{15} y^{3}

= \frac{64 x ^{15} y ^{3}}{( 16 x y ^{4} ) ^{3}}

Simplify

(16 x y^{4})^{3} : 4096 x^{3} y^{12}

= \frac{64 x ^{15} y ^{3}}{4096 x ^{3} y ^{12}}

Cancel the common factor:

64

= \frac{x ^{15} y ^{3}}{64 x ^{3} y ^{12}}

Apply exponent rule:

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

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

= \frac{y ^{3} x ^{15 - 3}}{64 y ^{12}}

Subtract the numbers:

15 - 3 = 12

= \frac{x ^{12} y ^{3}}{64 y ^{12}}

Apply exponent rule:

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

\frac{y ^{3}}{y ^{12}} = \frac{1}{y ^{12 - 3}}

= \frac{x ^{12}}{64 y ^{12 - 3}}

Subtract the numbers:

12 - 3 = 9

= \frac{x ^{12}}{64 y ^{9}}

- \frac{5}{5}

3 x + 1 = 16 - 2 x

- 6 x + 70 > - 2

5 q > 10

What is ((4x^5y)/(16xy^4))^3 ?
The solution to ((4x^5y)/(16xy^4))^3 is (x^{12})/(64y^9)