Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

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

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

Step 1.1.2

Cancel the common factors.

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Step 1.1.2.1

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

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

Step 1.1.2.2

Cancel the common factor.

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

Step 1.1.2.3

Rewrite the expression.

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

Step 1.2

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

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Step 1.2.1

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

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

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

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

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

Step 1.2.2.2

Cancel the common factor.

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

Step 1.2.2.3

Rewrite the expression.

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

Step 1.3

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

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Step 1.3.1

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

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

Step 1.3.2

Multiply $2$ by $3$ .

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

Step 2

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

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

Step 3

Combine the numerators over the common denominator.

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