Algebra Examples

$\frac{3 y^{7}}{{(2 y^{- 2})}^{- 5}}$

Step 1

Move ${(2 y^{- 2})}^{- 5}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$3 y^{7} {(2 y^{- 2})}^{5}$

Step 2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$3 y^{7} {(2 \frac{1}{y^{2}})}^{5}$

Step 3

Combine $2$ and $\frac{1}{y^{2}}$ .

$3 y^{7} {(\frac{2}{y^{2}})}^{5}$

Step 4

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

$3 y^{7} \frac{2^{5}}{{(y^{2})}^{5}}$

Step 5

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

$3 y^{7} \frac{32}{{(y^{2})}^{5}}$

Step 6

Multiply the exponents in ${(y^{2})}^{5}$ .

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Step 6.1

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

$3 y^{7} \frac{32}{y^{2 \cdot 5}}$

Step 6.2

Multiply $2$ by $5$ .

$3 y^{7} \frac{32}{y^{10}}$

Step 7

Cancel the common factor of $y^{7}$ .

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Step 7.1

Factor $y^{7}$ out of $3 y^{7}$ .

$y^{7} \cdot 3 \frac{32}{y^{10}}$

Step 7.2

Factor $y^{7}$ out of $y^{10}$ .

$y^{7} \cdot 3 \frac{32}{y^{7} y^{3}}$

Step 7.3

Cancel the common factor.

$y^{7} \cdot 3 \frac{32}{y^{7} y^{3}}$

Step 7.4

Rewrite the expression.

$3 \frac{32}{y^{3}}$

Step 8

Combine $3$ and $\frac{32}{y^{3}}$ .

$\frac{3 \cdot 32}{y^{3}}$

Step 9

Multiply $3$ by $32$ .

$\frac{96}{y^{3}}$