Algebra Examples

$\frac{5 a^{- 4} a^{6} b^{- 5}}{15 a^{- 2} b^{6}}$

Step 1

Multiply $a^{- 4}$ by $a^{6}$ by adding the exponents.

Tap for more steps...

Step 1.1

Move $a^{6}$ .

$\frac{5 (a^{6} a^{- 4}) b^{- 5}}{15 a^{- 2} b^{6}}$

Step 1.2

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

$\frac{5 a^{6 - 4} b^{- 5}}{15 a^{- 2} b^{6}}$

Step 1.3

Subtract $4$ from $6$ .

$\frac{5 a^{2} b^{- 5}}{15 a^{- 2} b^{6}}$

Step 2

Move $b^{- 5}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{5 a^{2}}{15 a^{- 2} b^{6} b^{5}}$

Step 3

Multiply $b^{6}$ by $b^{5}$ by adding the exponents.

Tap for more steps...

Step 3.1

Move $b^{5}$ .

$\frac{5 a^{2}}{15 a^{- 2} (b^{5} b^{6})}$

Step 3.2

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

$\frac{5 a^{2}}{15 a^{- 2} b^{5 + 6}}$

Step 3.3

Add $5$ and $6$ .

$\frac{5 a^{2}}{15 a^{- 2} b^{11}}$

Step 4

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

$\frac{5 a^{2} a^{2}}{15 b^{11}}$

Step 5

Multiply $a^{2}$ by $a^{2}$ by adding the exponents.

Tap for more steps...

Step 5.1

Move $a^{2}$ .

$\frac{5 (a^{2} a^{2})}{15 b^{11}}$

Step 5.2

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

$\frac{5 a^{2 + 2}}{15 b^{11}}$

Step 5.3

Add $2$ and $2$ .

$\frac{5 a^{4}}{15 b^{11}}$

Step 6

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

Tap for more steps...

Step 6.1

Factor $5$ out of $5 a^{4}$ .

$\frac{5 (a^{4})}{15 b^{11}}$

Step 6.2

Cancel the common factors.

Tap for more steps...

Step 6.2.1

Factor $5$ out of $15 b^{11}$ .

$\frac{5 (a^{4})}{5 (3 b^{11})}$

Step 6.2.2

Cancel the common factor.

$\frac{5 a^{4}}{5 (3 b^{11})}$

Step 6.2.3

Rewrite the expression.

$\frac{a^{4}}{3 b^{11}}$