Basic Math Examples

${(\frac{12 n y^{4}}{16 n^{- 3 y^{5}}})}^{- 2}$

Step 1

Cancel the common factor of $12$ and $16$ .

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Step 1.1

Factor $4$ out of $12 n y^{4}$ .

${(\frac{4 (3 n y^{4})}{16 n^{- 3 y^{5}}})}^{- 2}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $4$ out of $16 n^{- 3 y^{5}}$ .

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

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

Step 2

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

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

Step 3

Cancel the common factor of $n^{- 3 y^{5}}$ and $n$ .

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Step 3.1

Factor $n$ out of $4 n^{- 3 y^{5}}$ .

${(\frac{n (4 n^{- 3 y^{5} - 1})}{3 n y^{4}})}^{2}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $n$ out of $3 n y^{4}$ .

${(\frac{n (4 n^{- 3 y^{5} - 1})}{n (3 y^{4})})}^{2}$

Step 3.2.2

Cancel the common factor.

${(\frac{n (4 n^{- 3 y^{5} - 1})}{n (3 y^{4})})}^{2}$

Step 3.2.3

Rewrite the expression.

${(\frac{4 n^{- 3 y^{5} - 1}}{3 y^{4}})}^{2}$

Step 4

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 4.1

Apply the product rule to $\frac{4 n^{- 3 y^{5} - 1}}{3 y^{4}}$ .

$\frac{{(4 n^{- 3 y^{5} - 1})}^{2}}{{(3 y^{4})}^{2}}$

Step 4.2

Apply the product rule to $4 n^{- 3 y^{5} - 1}$ .

$\frac{4^{2} {(n^{- 3 y^{5} - 1})}^{2}}{{(3 y^{4})}^{2}}$

Step 4.3

Apply the product rule to $3 y^{4}$ .

$\frac{4^{2} {(n^{- 3 y^{5} - 1})}^{2}}{3^{2} {(y^{4})}^{2}}$

Step 5

Simplify the numerator.

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Step 5.1

Raise $4$ to the power of $2$ .

$\frac{16 {(n^{- 3 y^{5} - 1})}^{2}}{3^{2} {(y^{4})}^{2}}$

Step 5.2

Multiply the exponents in ${(n^{- 3 y^{5} - 1})}^{2}$ .

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Step 5.2.1

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

$\frac{16 n^{(- 3 y^{5} - 1) \cdot 2}}{3^{2} {(y^{4})}^{2}}$

Step 5.2.2

Apply the distributive property.

$\frac{16 n^{- 3 y^{5} \cdot 2 - 1 \cdot 2}}{3^{2} {(y^{4})}^{2}}$

Step 5.2.3

Multiply $2$ by $- 3$ .

$\frac{16 n^{- 6 y^{5} - 1 \cdot 2}}{3^{2} {(y^{4})}^{2}}$

Step 5.2.4

Multiply $- 1$ by $2$ .

$\frac{16 n^{- 6 y^{5} - 2}}{3^{2} {(y^{4})}^{2}}$

Step 6

Simplify the denominator.

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Step 6.1

Raise $3$ to the power of $2$ .

$\frac{16 n^{- 6 y^{5} - 2}}{9 {(y^{4})}^{2}}$

Step 6.2

Multiply the exponents in ${(y^{4})}^{2}$ .

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Step 6.2.1

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

$\frac{16 n^{- 6 y^{5} - 2}}{9 y^{4 \cdot 2}}$

Step 6.2.2

Multiply $4$ by $2$ .

$\frac{16 n^{- 6 y^{5} - 2}}{9 y^{8}}$