Simplify (ab^3)/(a^4b)+(c^2)^3

$\frac{a b^{3}}{a^{4} b} + {(c^{2})}^{3}$

Simplify each term.

Cancel the common factor of $a$ and $a^{4}$ .

Factor $a$ out of $a b^{3}$ .

$\frac{a (b^{3})}{a^{4} b} + {(c^{2})}^{3}$

Cancel the common factors.

Factor $a$ out of $a^{4} b$ .

$\frac{a (b^{3})}{a (a^{3} b)} + {(c^{2})}^{3}$

Cancel the common factor.

$\frac{a b^{3}}{a (a^{3} b)} + {(c^{2})}^{3}$

Rewrite the expression.

$\frac{b^{3}}{a^{3} b} + {(c^{2})}^{3}$

Cancel the common factor of $b^{3}$ and $b$ .

Factor $b$ out of $b^{3}$ .

$\frac{b \cdot b^{2}}{a^{3} b} + {(c^{2})}^{3}$

Cancel the common factors.

Factor $b$ out of $a^{3} b$ .

$\frac{b \cdot b^{2}}{b a^{3}} + {(c^{2})}^{3}$

Cancel the common factor.

$\frac{b \cdot b^{2}}{b a^{3}} + {(c^{2})}^{3}$

Rewrite the expression.

$\frac{b^{2}}{a^{3}} + {(c^{2})}^{3}$

Multiply the exponents in ${(c^{2})}^{3}$ .

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{b^{2}}{a^{3}} + c^{2 \cdot 3}$

Multiply $2$ by $3$ .

$\frac{b^{2}}{a^{3}} + c^{6}$

To write $c^{6}$ as a fraction with a common denominator, multiply by $\frac{a^{3}}{a^{3}}$ .

$\frac{b^{2}}{a^{3}} + \frac{c^{6} a^{3}}{a^{3}}$

Combine the numerators over the common denominator.

$\frac{b^{2} + c^{6} a^{3}}{a^{3}}$