Basic Math Examples

${(9 a^{5} n^{2} \div 6 y^{7} n^{5})}^{- 1} \cdot (12 a^{3} n \div y^{2} n^{4})$

Step 1

Rewrite the division as a fraction.

${(\frac{9 a^{5} n^{2}}{6 y^{7} n^{5}})}^{- 1} \cdot 12 a^{3} n \div y^{2} n^{4}$

Step 2

Cancel the common factor of $9$ and $6$ .

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Step 2.1

Factor $3$ out of $9 a^{5} n^{2}$ .

${(\frac{3 (3 a^{5} n^{2})}{6 y^{7} n^{5}})}^{- 1} \cdot 12 a^{3} n \div y^{2} n^{4}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $3$ out of $6 y^{7} n^{5}$ .

${(\frac{3 (3 a^{5} n^{2})}{3 (2 y^{7} n^{5})})}^{- 1} \cdot 12 a^{3} n \div y^{2} n^{4}$

Step 2.2.2

Cancel the common factor.

${(\frac{3 (3 a^{5} n^{2})}{3 (2 y^{7} n^{5})})}^{- 1} \cdot 12 a^{3} n \div y^{2} n^{4}$

Step 2.2.3

Rewrite the expression.

${(\frac{3 a^{5} n^{2}}{2 y^{7} n^{5}})}^{- 1} \cdot 12 a^{3} n \div y^{2} n^{4}$

Step 3

Cancel the common factor of $n^{2}$ and $n^{5}$ .

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Step 3.1

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

${(\frac{n^{2} (3 a^{5})}{2 y^{7} n^{5}})}^{- 1} \cdot 12 a^{3} n \div y^{2} n^{4}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $n^{2}$ out of $2 y^{7} n^{5}$ .

${(\frac{n^{2} (3 a^{5})}{n^{2} (2 y^{7} n^{3})})}^{- 1} \cdot 12 a^{3} n \div y^{2} n^{4}$

Step 3.2.2

Cancel the common factor.

${(\frac{n^{2} (3 a^{5})}{n^{2} (2 y^{7} n^{3})})}^{- 1} \cdot 12 a^{3} n \div y^{2} n^{4}$

Step 3.2.3

Rewrite the expression.

${(\frac{3 a^{5}}{2 y^{7} n^{3}})}^{- 1} \cdot 12 a^{3} n \div y^{2} n^{4}$

Step 4

Change the sign of the exponent by rewriting the base as its reciprocal.

$\frac{2 y^{7} n^{3}}{3 a^{5}} \cdot 12 a^{3} n \div y^{2} n^{4}$

Step 5

Combine.

$\frac{2 y^{7} n^{3} (12 a^{3} n)}{3 a^{5} (y^{2} n^{4})}$

Step 6

Multiply $n^{3}$ by $n$ by adding the exponents.

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Step 6.1

Move $n$ .

$\frac{2 y^{7} (n \cdot n^{3}) (12 a^{3})}{3 a^{5} (y^{2} n^{4})}$

Step 6.2

Multiply $n$ by $n^{3}$ .

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Step 6.2.1

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

$\frac{2 y^{7} (n^{1} n^{3}) (12 a^{3})}{3 a^{5} (y^{2} n^{4})}$

Step 6.2.2

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

$\frac{2 y^{7} n^{1 + 3} (12 a^{3})}{3 a^{5} (y^{2} n^{4})}$

Step 6.3

Add $1$ and $3$ .

$\frac{2 y^{7} n^{4} (12 a^{3})}{3 a^{5} (y^{2} n^{4})}$

Step 7

Cancel the common factor of $y^{7}$ and $y^{2}$ .

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Step 7.1

Factor $y^{2}$ out of $2 y^{7} n^{4} (12 a^{3})$ .

$\frac{y^{2} (2 y^{5} n^{4} (12 a^{3}))}{3 a^{5} (y^{2} n^{4})}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

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

$\frac{y^{2} (2 y^{5} n^{4} (12 a^{3}))}{y^{2} (3 a^{5} (n^{4}))}$

Step 7.2.2

Cancel the common factor.

$\frac{y^{2} (2 y^{5} n^{4} (12 a^{3}))}{y^{2} (3 a^{5} (n^{4}))}$

Step 7.2.3

Rewrite the expression.

$\frac{2 y^{5} n^{4} (12 a^{3})}{3 a^{5} (n^{4})}$

Step 8

Cancel the common factor of $n^{4}$ .

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Step 8.1

Cancel the common factor.

$\frac{2 y^{5} n^{4} (12 a^{3})}{3 a^{5} n^{4}}$

Step 8.2

Rewrite the expression.

$\frac{2 y^{5} (12 a^{3})}{3 a^{5}}$

Step 9

Cancel the common factor of $12$ and $3$ .

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Step 9.1

Factor $3$ out of $2 y^{5} (12 a^{3})$ .

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

Step 9.2

Cancel the common factors.

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Step 9.2.1

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

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

Step 9.2.2

Cancel the common factor.

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

Step 9.2.3

Rewrite the expression.

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

Step 10

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

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Step 10.1

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

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

Step 10.2

Cancel the common factors.

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Step 10.2.1

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

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

Step 10.2.2

Cancel the common factor.

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

Step 10.2.3

Rewrite the expression.

$\frac{2 y^{5} \cdot (4)}{a^{2}}$

Step 11

Multiply $4$ by $2$ .

$\frac{8 y^{5}}{a^{2}}$