Algebra Examples

$\frac{8 a^{3} {(b^{5})}^{2}}{2 a^{5} b^{3}}$

Step 1

Cancel the common factor of $8$ and $2$ .

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Step 1.1

Factor $2$ out of $8 a^{3} {(b^{5})}^{2}$ .

$\frac{2 (4 a^{3} {(b^{5})}^{2})}{2 a^{5} b^{3}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $2$ out of $2 a^{5} b^{3}$ .

$\frac{2 (4 a^{3} {(b^{5})}^{2})}{2 (a^{5} b^{3})}$

Step 1.2.2

Cancel the common factor.

$\frac{2 (4 a^{3} {(b^{5})}^{2})}{2 (a^{5} b^{3})}$

Step 1.2.3

Rewrite the expression.

$\frac{4 a^{3} {(b^{5})}^{2}}{a^{5} b^{3}}$

Step 2

Cancel the common factor of $a^{3}$ and $a^{5}$ .

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Step 2.1

Factor $a^{3}$ out of $4 a^{3} {(b^{5})}^{2}$ .

$\frac{a^{3} (4 {(b^{5})}^{2})}{a^{5} b^{3}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $a^{3}$ out of $a^{5} b^{3}$ .

$\frac{a^{3} (4 {(b^{5})}^{2})}{a^{3} (a^{2} b^{3})}$

Step 2.2.2

Cancel the common factor.

$\frac{a^{3} (4 {(b^{5})}^{2})}{a^{3} (a^{2} b^{3})}$

Step 2.2.3

Rewrite the expression.

$\frac{4 {(b^{5})}^{2}}{a^{2} b^{3}}$

Step 3

Multiply the exponents in ${(b^{5})}^{2}$ .

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Step 3.1

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

$\frac{4 b^{5 \cdot 2}}{a^{2} b^{3}}$

Step 3.2

Multiply $5$ by $2$ .

$\frac{4 b^{10}}{a^{2} b^{3}}$

Step 4

Cancel the common factor of $b^{10}$ and $b^{3}$ .

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Step 4.1

Factor $b^{3}$ out of $4 b^{10}$ .

$\frac{b^{3} (4 b^{7})}{a^{2} b^{3}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $b^{3}$ out of $a^{2} b^{3}$ .

$\frac{b^{3} (4 b^{7})}{b^{3} a^{2}}$

Step 4.2.2

Cancel the common factor.

$\frac{b^{3} (4 b^{7})}{b^{3} a^{2}}$

Step 4.2.3

Rewrite the expression.

$\frac{4 b^{7}}{a^{2}}$