Pre-Algebra Examples

$\frac{9 y^{- 4}}{3 y^{- 7}}$

Step 1

Move $y^{- 7}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{9 y^{- 4} y^{7}}{3}$

Step 2

Multiply $y^{- 4}$ by $y^{7}$ by adding the exponents.

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Step 2.1

Move $y^{7}$ .

$\frac{9 (y^{7} y^{- 4})}{3}$

Step 2.2

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

$\frac{9 y^{7 - 4}}{3}$

Step 2.3

Subtract $4$ from $7$ .

$\frac{9 y^{3}}{3}$

Step 3

Cancel the common factor of $9$ and $3$ .

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Step 3.1

Factor $3$ out of $9 y^{3}$ .

$\frac{3 (3 y^{3})}{3}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $3$ out of $3$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

$\frac{3 y^{3}}{1}$

Step 3.2.4

Divide $3 y^{3}$ by $1$ .

$3 y^{3}$