Basic Math Examples

$\frac{4 a b^{9}}{7 a^{6} b} \div \frac{32 a^{6} b^{6}}{56 a b^{9}}$

Step 1

To divide by a fraction, multiply by its reciprocal.

$\frac{4 a b^{9}}{7 a^{6} b} \cdot \frac{56 a b^{9}}{32 a^{6} b^{6}}$

Step 2

Combine.

$\frac{4 a b^{9} (56 a b^{9})}{7 a^{6} b (32 a^{6} b^{6})}$

Step 3

Multiply $a$ by $a$ by adding the exponents.

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Step 3.1

Move $a$ .

$\frac{4 (a \cdot a) b^{9} (56 b^{9})}{7 a^{6} b (32 a^{6} b^{6})}$

Step 3.2

Multiply $a$ by $a$ .

$\frac{4 a^{2} b^{9} (56 b^{9})}{7 a^{6} b (32 a^{6} b^{6})}$

Step 4

Multiply $b^{9}$ by $b^{9}$ by adding the exponents.

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Step 4.1

Move $b^{9}$ .

$\frac{4 a^{2} (b^{9} b^{9}) \cdot 56}{7 a^{6} b (32 a^{6} b^{6})}$

Step 4.2

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

$\frac{4 a^{2} b^{9 + 9} \cdot 56}{7 a^{6} b (32 a^{6} b^{6})}$

Step 4.3

Add $9$ and $9$ .

$\frac{4 a^{2} b^{18} \cdot 56}{7 a^{6} b (32 a^{6} b^{6})}$

Step 5

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

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Step 5.1

Move $a^{6}$ .

$\frac{4 a^{2} b^{18} \cdot 56}{7 (a^{6} a^{6}) b (32 b^{6})}$

Step 5.2

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

$\frac{4 a^{2} b^{18} \cdot 56}{7 a^{6 + 6} b (32 b^{6})}$

Step 5.3

Add $6$ and $6$ .

$\frac{4 a^{2} b^{18} \cdot 56}{7 a^{12} b (32 b^{6})}$

Step 6

Multiply $b$ by $b^{6}$ by adding the exponents.

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Step 6.1

Move $b^{6}$ .

$\frac{4 a^{2} b^{18} \cdot 56}{7 a^{12} (b^{6} b) \cdot 32}$

Step 6.2

Multiply $b^{6}$ by $b$ .

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Step 6.2.1

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

$\frac{4 a^{2} b^{18} \cdot 56}{7 a^{12} (b^{6} b^{1}) \cdot 32}$

Step 6.2.2

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

$\frac{4 a^{2} b^{18} \cdot 56}{7 a^{12} b^{6 + 1} \cdot 32}$

Step 6.3

Add $6$ and $1$ .

$\frac{4 a^{2} b^{18} \cdot 56}{7 a^{12} b^{7} \cdot 32}$

Step 7

Cancel the common factor of $4$ and $32$ .

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Step 7.1

Factor $4$ out of $4 a^{2} b^{18} \cdot 56$ .

$\frac{4 (a^{2} b^{18} \cdot 56)}{7 a^{12} b^{7} \cdot 32}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $4$ out of $7 a^{12} b^{7} \cdot 32$ .

$\frac{4 (a^{2} b^{18} \cdot 56)}{4 (7 a^{12} b^{7} \cdot 8)}$

Step 7.2.2

Cancel the common factor.

$\frac{4 (a^{2} b^{18} \cdot 56)}{4 (7 a^{12} b^{7} \cdot 8)}$

Step 7.2.3

Rewrite the expression.

$\frac{a^{2} b^{18} \cdot 56}{7 a^{12} b^{7} \cdot 8}$

Step 8

Cancel the common factor of $a^{2}$ and $a^{12}$ .

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Step 8.1

Factor $a^{2}$ out of $a^{2} b^{18} \cdot 56$ .

$\frac{a^{2} (b^{18} \cdot 56)}{7 a^{12} b^{7} \cdot 8}$

Step 8.2

Cancel the common factors.

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Step 8.2.1

Factor $a^{2}$ out of $7 a^{12} b^{7} \cdot 8$ .

$\frac{a^{2} (b^{18} \cdot 56)}{a^{2} (7 a^{10} b^{7} \cdot 8)}$

Step 8.2.2

Cancel the common factor.

$\frac{a^{2} (b^{18} \cdot 56)}{a^{2} (7 a^{10} b^{7} \cdot 8)}$

Step 8.2.3

Rewrite the expression.

$\frac{b^{18} \cdot 56}{7 a^{10} b^{7} \cdot 8}$

Step 9

Cancel the common factor of $b^{18}$ and $b^{7}$ .

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Step 9.1

Factor $b^{7}$ out of $b^{18} \cdot 56$ .

$\frac{b^{7} (b^{11} \cdot 56)}{7 a^{10} b^{7} \cdot 8}$

Step 9.2

Cancel the common factors.

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Step 9.2.1

Factor $b^{7}$ out of $7 a^{10} b^{7} \cdot 8$ .

$\frac{b^{7} (b^{11} \cdot 56)}{b^{7} (7 a^{10} \cdot 8)}$

Step 9.2.2

Cancel the common factor.

$\frac{b^{7} (b^{11} \cdot 56)}{b^{7} (7 a^{10} \cdot 8)}$

Step 9.2.3

Rewrite the expression.

$\frac{b^{11} \cdot 56}{7 a^{10} \cdot 8}$

Step 10

Cancel the common factor of $56$ and $7$ .

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Step 10.1

Factor $7$ out of $b^{11} \cdot 56$ .

$\frac{7 (b^{11} \cdot 8)}{7 a^{10} \cdot 8}$

Step 10.2

Cancel the common factors.

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Step 10.2.1

Factor $7$ out of $7 a^{10} \cdot 8$ .

$\frac{7 (b^{11} \cdot 8)}{7 (a^{10} \cdot 8)}$

Step 10.2.2

Cancel the common factor.

$\frac{7 (b^{11} \cdot 8)}{7 (a^{10} \cdot 8)}$

Step 10.2.3

Rewrite the expression.

$\frac{b^{11} \cdot 8}{a^{10} \cdot 8}$

Step 11

Cancel the common factor of $8$ .

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Step 11.1

Cancel the common factor.

$\frac{b^{11} \cdot 8}{a^{10} \cdot 8}$

Step 11.2

Rewrite the expression.

$\frac{b^{11}}{a^{10}}$