Basic Math Examples

${(\frac{5 y^{2}}{15 y^{4}})}^{- 2}$

Step 1

Cancel the common factor of $5$ and $15$ .

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Step 1.1

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

${(\frac{5 (y^{2})}{15 y^{4}})}^{- 2}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $5$ out of $15 y^{4}$ .

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

Step 1.2.2

Cancel the common factor.

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

Step 1.2.3

Rewrite the expression.

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

Step 2

Cancel the common factor of $y^{2}$ and $y^{4}$ .

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Step 2.1

Multiply by $1$ .

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $y^{2}$ out of $3 y^{4}$ .

${(\frac{y^{2} \cdot 1}{y^{2} (3 y^{2})})}^{- 2}$

Step 2.2.2

Cancel the common factor.

${(\frac{y^{2} \cdot 1}{y^{2} (3 y^{2})})}^{- 2}$

Step 2.2.3

Rewrite the expression.

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

Step 3

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

${(3 y^{2})}^{2}$

Step 4

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

$3^{2} {(y^{2})}^{2}$

Step 5

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

$9 {(y^{2})}^{2}$

Step 6

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

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Step 6.1

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

$9 y^{2 \cdot 2}$

Step 6.2

Multiply $2$ by $2$ .

$9 y^{4}$