What is ((a^2b)/(ab^3))^2 ?

The solution to ((a^2b)/(ab^3))^2 is (a^2)/(b^4)

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simplify ((a^2b)/(ab^3))^2

simplify

(\frac{a ^{2} b}{a b ^{3}})^{2}

\frac{a ^{2}}{b ^{4}}

Solution steps

(\frac{a ^{2} b}{a b ^{3}})^{2}

Apply exponent rule:

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

= \frac{( a ^{2} b ) ^{2}}{( a b ^{3} ) ^{2}}

Simplify

(a^{2} b)^{2} : a^{4} b^{2}

= \frac{a ^{4} b ^{2}}{( a b ^{3} ) ^{2}}

Simplify

(a b^{3})^{2} : a^{2} b^{6}

= \frac{a ^{4} b ^{2}}{a ^{2} b ^{6}}

Apply exponent rule:

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

\frac{a ^{4}}{a ^{2}} = a^{4 - 2}

= \frac{b ^{2} a ^{4 - 2}}{b ^{6}}

Subtract the numbers:

4 - 2 = 2

= \frac{a ^{2} b ^{2}}{b ^{6}}

Apply exponent rule:

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

\frac{b ^{2}}{b ^{6}} = \frac{1}{b ^{6 - 2}}

= \frac{a ^{2}}{b ^{6 - 2}}

Subtract the numbers:

6 - 2 = 4

= \frac{a ^{2}}{b ^{4}}

(5 x - 6) (x + 2)

- \frac{1}{2} 3

19 x - 3 (5 x - 2)

2 (\frac{7}{2})

\frac{36}{108}