Basic Math Examples

$\frac{a^{8} b \cdot (a^{6} b^{2})}{{(a^{2} b^{5})}^{2}}$

Step 1

Multiply $a^{8}$ by $a^{6}$ by adding the exponents.

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Step 1.1

Move $a^{6}$ .

$\frac{a^{6} a^{8} b \cdot b^{2}}{{(a^{2} b^{5})}^{2}}$

Step 1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{a^{6 + 8} b \cdot b^{2}}{{(a^{2} b^{5})}^{2}}$

Step 1.3

Add $6$ and $8$ .

$\frac{a^{14} b \cdot b^{2}}{{(a^{2} b^{5})}^{2}}$

Step 2

Multiply $b$ by $b^{2}$ by adding the exponents.

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Step 2.1

Move $b^{2}$ .

$\frac{a^{14} (b^{2} b)}{{(a^{2} b^{5})}^{2}}$

Step 2.2

Multiply $b^{2}$ by $b$ .

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Step 2.2.1

Raise $b$ to the power of $1$ .

$\frac{a^{14} (b^{2} b^{1})}{{(a^{2} b^{5})}^{2}}$

Step 2.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{a^{14} b^{2 + 1}}{{(a^{2} b^{5})}^{2}}$

Step 2.3

Add $2$ and $1$ .

$\frac{a^{14} b^{3}}{{(a^{2} b^{5})}^{2}}$

Step 3

Simplify the denominator.

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Step 3.1

Apply the product rule to $a^{2} b^{5}$ .

$\frac{a^{14} b^{3}}{{(a^{2})}^{2} {(b^{5})}^{2}}$

Step 3.2

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

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Step 3.2.1

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

$\frac{a^{14} b^{3}}{a^{2 \cdot 2} {(b^{5})}^{2}}$

Step 3.2.2

Multiply $2$ by $2$ .

$\frac{a^{14} b^{3}}{a^{4} {(b^{5})}^{2}}$

Step 3.3

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

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Step 3.3.1

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

$\frac{a^{14} b^{3}}{a^{4} b^{5 \cdot 2}}$

Step 3.3.2

Multiply $5$ by $2$ .

$\frac{a^{14} b^{3}}{a^{4} b^{10}}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Cancel the common factor of $a^{14}$ and $a^{4}$ .

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Step 4.1.1

Factor $a^{4}$ out of $a^{14} b^{3}$ .

$\frac{a^{4} (a^{10} b^{3})}{a^{4} b^{10}}$

Step 4.1.2

Cancel the common factors.

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Step 4.1.2.1

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

$\frac{a^{4} (a^{10} b^{3})}{a^{4} (b^{10})}$

Step 4.1.2.2

Cancel the common factor.

$\frac{a^{4} (a^{10} b^{3})}{a^{4} b^{10}}$

Step 4.1.2.3

Rewrite the expression.

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

Step 4.2

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

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Step 4.2.1

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

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

Step 4.2.2

Cancel the common factors.

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Step 4.2.2.1

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

$\frac{b^{3} a^{10}}{b^{3} b^{7}}$

Step 4.2.2.2

Cancel the common factor.

$\frac{b^{3} a^{10}}{b^{3} b^{7}}$

Step 4.2.2.3

Rewrite the expression.

$\frac{a^{10}}{b^{7}}$