Basic Math Examples

$- 2 y n^{4} \div {(n^{2} y^{3})}^{3}$

Step 1

Rewrite the division as a fraction.

$\frac{- 2 y n^{4}}{{(n^{2} y^{3})}^{3}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $n^{2} y^{3}$ .

$\frac{- 2 y n^{4}}{{(n^{2})}^{3} {(y^{3})}^{3}}$

Step 2.2

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

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Step 2.2.1

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

$\frac{- 2 y n^{4}}{n^{2 \cdot 3} {(y^{3})}^{3}}$

Step 2.2.2

Multiply $2$ by $3$ .

$\frac{- 2 y n^{4}}{n^{6} {(y^{3})}^{3}}$

Step 2.3

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

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Step 2.3.1

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

$\frac{- 2 y n^{4}}{n^{6} y^{3 \cdot 3}}$

Step 2.3.2

Multiply $3$ by $3$ .

$\frac{- 2 y n^{4}}{n^{6} y^{9}}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $y$ and $y^{9}$ .

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Step 3.1.1

Factor $y$ out of $- 2 y n^{4}$ .

$\frac{y (- 2 n^{4})}{n^{6} y^{9}}$

Step 3.1.2

Cancel the common factors.

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Step 3.1.2.1

Factor $y$ out of $n^{6} y^{9}$ .

$\frac{y (- 2 n^{4})}{y (n^{6} y^{8})}$

Step 3.1.2.2

Cancel the common factor.

$\frac{y (- 2 n^{4})}{y (n^{6} y^{8})}$

Step 3.1.2.3

Rewrite the expression.

$\frac{- 2 n^{4}}{n^{6} y^{8}}$

Step 3.2

Cancel the common factor of $n^{4}$ and $n^{6}$ .

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Step 3.2.1

Factor $n^{4}$ out of $- 2 n^{4}$ .

$\frac{n^{4} \cdot - 2}{n^{6} y^{8}}$

Step 3.2.2

Cancel the common factors.

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Step 3.2.2.1

Factor $n^{4}$ out of $n^{6} y^{8}$ .

$\frac{n^{4} \cdot - 2}{n^{4} (n^{2} y^{8})}$

Step 3.2.2.2

Cancel the common factor.

$\frac{n^{4} \cdot - 2}{n^{4} (n^{2} y^{8})}$

Step 3.2.2.3

Rewrite the expression.

$\frac{- 2}{n^{2} y^{8}}$

Step 3.3

Move the negative in front of the fraction.

$- \frac{2}{n^{2} y^{8}}$