Finite Math Examples

$\frac{{(5 y^{7})}^{2}}{y^{- 4}}$

Step 1

Move $y^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

${(5 y^{7})}^{2} y^{4}$

Step 2

Apply the product rule to $5 y^{7}$ .

$5^{2} {(y^{7})}^{2} y^{4}$

Step 3

Raise $5$ to the power of $2$ .

$25 {(y^{7})}^{2} y^{4}$

Step 4

Multiply the exponents in ${(y^{7})}^{2}$ .

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Step 4.1

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

$25 y^{7 \cdot 2} y^{4}$

Step 4.2

Multiply $7$ by $2$ .

$25 y^{14} y^{4}$

Step 5

Multiply $y^{14}$ by $y^{4}$ by adding the exponents.

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Step 5.1

Move $y^{4}$ .

$25 (y^{4} y^{14})$

Step 5.2

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

$25 y^{4 + 14}$

Step 5.3

Add $4$ and $14$ .

$25 y^{18}$