Algebra Examples

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

Step 1

Simplify the numerator.

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Step 1.1

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

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Step 1.1.1

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

$- \frac{3 y^{- 2 \cdot 3}}{5 y^{2}}$

Step 1.1.2

Multiply $- 2$ by $3$ .

$- \frac{3 y^{- 6}}{5 y^{2}}$

Step 1.2

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

$- \frac{3 \frac{1}{y^{6}}}{5 y^{2}}$

Step 2

Combine $3$ and $\frac{1}{y^{6}}$ .

$- \frac{\frac{3}{y^{6}}}{5 y^{2}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

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

Step 4

Combine.

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

Step 5

Multiply $y^{6}$ by $y^{2}$ by adding the exponents.

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Step 5.1

Move $y^{2}$ .

$- \frac{3 \cdot 1}{y^{2} y^{6} \cdot 5}$

Step 5.2

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

$- \frac{3 \cdot 1}{y^{2 + 6} \cdot 5}$

Step 5.3

Add $2$ and $6$ .

$- \frac{3 \cdot 1}{y^{8} \cdot 5}$

Step 6

Multiply $3$ by $1$ .

$- \frac{3}{y^{8} \cdot 5}$

Step 7

Move $5$ to the left of $y^{8}$ .

$- \frac{3}{5 y^{8}}$