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

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

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

simplify

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

b^{3}

Solution steps

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

Apply exponent rule:

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

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

Simplify

(a b^{3})^{3} : a^{3} b^{9}

= \frac{a ^{3} b ^{9}}{( b ^{2} a ) ^{3}}

Simplify

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

= \frac{a ^{3} b ^{9}}{b ^{6} a ^{3}}

Cancel the common factor:

a^{3}

= \frac{b ^{9}}{b ^{6}}

Apply exponent rule:

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

\frac{b ^{9}}{b ^{6}} = b^{9 - 6}

= b^{9 - 6}

Subtract the numbers:

9 - 6 = 3

= b^{3}

32 b^{3}

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

x^{4} + 4 x^{2} + 4 x^{4} - 3 x^{2} - 10

x^{3} \cdot x^{7}