What is ((5x^3y)/(20xy^5))^4 ?

The solution to ((5x^3y)/(20xy^5))^4 is (x^8)/(256y^{16)}

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simplify ((5x^3y)/(20xy^5))^4

simplify

(\frac{5 x ^{3} y}{20 x y ^{5}})^{4}

\frac{x ^{8}}{256 y ^{16}}

Solution steps

(\frac{5 x ^{3} y}{20 x y ^{5}})^{4}

Apply exponent rule:

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

= \frac{( 5 x ^{3} y ) ^{4}}{( 20 x y ^{5} ) ^{4}}

Simplify

(5 x^{3} y)^{4} : 625 x^{12} y^{4}

= \frac{625 x ^{12} y ^{4}}{( 20 x y ^{5} ) ^{4}}

Simplify

(20 x y^{5})^{4} : 160000 x^{4} y^{20}

= \frac{625 x ^{12} y ^{4}}{160000 x ^{4} y ^{20}}

Cancel the common factor:

625

= \frac{x ^{12} y ^{4}}{256 x ^{4} y ^{20}}

Apply exponent rule:

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

\frac{x ^{12}}{x ^{4}} = x^{12 - 4}

= \frac{y ^{4} x ^{12 - 4}}{256 y ^{20}}

Subtract the numbers:

12 - 4 = 8

= \frac{x ^{8} y ^{4}}{256 y ^{20}}

Apply exponent rule:

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

\frac{y ^{4}}{y ^{20}} = \frac{1}{y ^{20 - 4}}

= \frac{x ^{8}}{256 y ^{20 - 4}}

Subtract the numbers:

20 - 4 = 16

= \frac{x ^{8}}{256 y ^{16}}

64 + x^{3}

(10 - 4)^{3} \div 9 \cdot 3 \div 6 + 10

\frac{2 ( x - 1 )}{3} = \frac{3 ( 2 x - 1 )}{2}

- 1 + 4 a - 4 a^{2}

7 (\frac{x}{2} - (\frac{x}{3} - (\frac{x}{4} + 5))) = 140

What is ((5x^3y)/(20xy^5))^4 ?
The solution to ((5x^3y)/(20xy^5))^4 is (x^8)/(256y^{16)}