What is (36x^4y^5)/((3xy)^2) ?

The solution to (36x^4y^5)/((3xy)^2) is 4x^2y^3

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simplify (36x^4y^5)/((3xy)^2)

simplify

\frac{36 x ^{4} y ^{5}}{( 3 x y ) ^{2}}

4 x^{2} y^{3}

Solution steps

\frac{36 x ^{4} y ^{5}}{( 3 x y ) ^{2}}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

(3 x y)^{2} = 3^{2} x^{2} y^{2}

= \frac{36 x ^{4} y ^{5}}{3 ^{2} x ^{2} y ^{2}}

Factor

36 : 3^{2} \cdot 4

= \frac{3 ^{2} \cdot 4 x ^{4} y ^{5}}{3 ^{2} x ^{2} y ^{2}}

Cancel the common factor:

3^{2}

= \frac{4 x ^{4} y ^{5}}{x ^{2} y ^{2}}

Simplify

\frac{x ^{4}}{x ^{2}} : x^{2}

= \frac{4 x ^{2} y ^{5}}{y ^{2}}

Simplify

\frac{y ^{5}}{y ^{2}} : y^{3}

= 4 x^{2} y^{3}

(\frac{5}{3})^{4}

(a - 3 b) - 3 (a - 2 b)

6 x^{2} - 9 x + 18

6 x^{4} + 2 x^{3}