What is ((x^4y^7)/(x^3y))^5 ?

The solution to ((x^4y^7)/(x^3y))^5 is x^5y^{30}

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simplify ((x^4y^7)/(x^3y))^5

simplify

(\frac{x ^{4} y ^{7}}{x ^{3} y})^{5}

x^{5} y^{30}

Solution steps

(\frac{x ^{4} y ^{7}}{x ^{3} y})^{5}

Apply exponent rule:

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

= \frac{( x ^{4} y ^{7} ) ^{5}}{( x ^{3} y ) ^{5}}

Simplify

(x^{4} y^{7})^{5} : x^{20} y^{35}

= \frac{x ^{20} y ^{35}}{( x ^{3} y ) ^{5}}

Simplify

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

= \frac{x ^{20} y ^{35}}{x ^{15} y ^{5}}

Apply exponent rule:

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

\frac{x ^{20}}{x ^{15}} = x^{20 - 15}

= \frac{y ^{35} x ^{20 - 15}}{y ^{5}}

Subtract the numbers:

20 - 15 = 5

= \frac{x ^{5} y ^{35}}{y ^{5}}

Apply exponent rule:

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

\frac{y ^{35}}{y ^{5}} = y^{35 - 5}

= x^{5} y^{35 - 5}

Subtract the numbers:

35 - 5 = 30

= x^{5} y^{30}

(- \frac{3}{4})^{- 4}

25 x^{4} - 81 y^{2}

\frac{6}{5} x - \frac{1}{3} > 2 x + 3

x^{3} y - 25 x y^{3}

\frac{x ^{2} - 2 x - 5}{x ^{2} + 4 x - 7} < 1