Basic Math Examples

${(\frac{13 y^{- 3}}{y^{5}})}^{- 2} \cdot \frac{4}{y^{5}}$

Step 1

Move $y^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

${(\frac{13}{y^{5} y^{3}})}^{- 2} \cdot \frac{4}{y^{5}}$

Step 2

Multiply $y^{5}$ by $y^{3}$ by adding the exponents.

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Step 2.1

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

${(\frac{13}{y^{5 + 3}})}^{- 2} \cdot \frac{4}{y^{5}}$

Step 2.2

Add $5$ and $3$ .

${(\frac{13}{y^{8}})}^{- 2} \cdot \frac{4}{y^{5}}$

Step 3

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

${(\frac{y^{8}}{13})}^{2} \cdot \frac{4}{y^{5}}$

Step 4

Apply the product rule to $\frac{y^{8}}{13}$ .

$\frac{{(y^{8})}^{2}}{13^{2}} \cdot \frac{4}{y^{5}}$

Step 5

Combine.

$\frac{{(y^{8})}^{2} \cdot 4}{13^{2} y^{5}}$

Step 6

Simplify the expression.

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Step 6.1

Multiply the exponents in ${(y^{8})}^{2}$ .

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Step 6.1.1

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

$\frac{y^{8 \cdot 2} \cdot 4}{13^{2} y^{5}}$

Step 6.1.2

Multiply $8$ by $2$ .

$\frac{y^{16} \cdot 4}{13^{2} y^{5}}$

Step 6.2

Raise $13$ to the power of $2$ .

$\frac{y^{16} \cdot 4}{169 y^{5}}$

Step 7

Cancel the common factor of $y^{16}$ and $y^{5}$ .

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Step 7.1

Factor $y^{5}$ out of $y^{16} \cdot 4$ .

$\frac{y^{5} (y^{11} \cdot 4)}{169 y^{5}}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $y^{5}$ out of $169 y^{5}$ .

$\frac{y^{5} (y^{11} \cdot 4)}{y^{5} \cdot 169}$

Step 7.2.2

Cancel the common factor.

$\frac{y^{5} (y^{11} \cdot 4)}{y^{5} \cdot 169}$

Step 7.2.3

Rewrite the expression.

$\frac{y^{11} \cdot 4}{169}$

Step 8

Move $4$ to the left of $y^{11}$ .

$\frac{4 y^{11}}{169}$