Algebra Examples

$\frac{3 b a^{- 4} \cdot a^{- 1} b^{4}}{3 a^{- 2} b^{- 3}}$

Step 1

Multiply $b$ by $b^{4}$ by adding the exponents.

Tap for more steps...

Step 1.1

Move $b^{4}$ .

$\frac{3 (b^{4} b) a^{- 4} \cdot a^{- 1}}{3 a^{- 2} b^{- 3}}$

Step 1.2

Multiply $b^{4}$ by $b$ .

Tap for more steps...

Step 1.2.1

Raise $b$ to the power of $1$ .

$\frac{3 (b^{4} b^{1}) a^{- 4} \cdot a^{- 1}}{3 a^{- 2} b^{- 3}}$

Step 1.2.2

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

$\frac{3 b^{4 + 1} a^{- 4} \cdot a^{- 1}}{3 a^{- 2} b^{- 3}}$

Step 1.3

Add $4$ and $1$ .

$\frac{3 b^{5} a^{- 4} \cdot a^{- 1}}{3 a^{- 2} b^{- 3}}$

Step 2

Multiply $a^{- 4}$ by $a^{- 1}$ by adding the exponents.

Tap for more steps...

Step 2.1

Move $a^{- 1}$ .

$\frac{3 b^{5} (a^{- 1} a^{- 4})}{3 a^{- 2} b^{- 3}}$

Step 2.2

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

$\frac{3 b^{5} a^{- 1 - 4}}{3 a^{- 2} b^{- 3}}$

Step 2.3

Subtract $4$ from $- 1$ .

$\frac{3 b^{5} a^{- 5}}{3 a^{- 2} b^{- 3}}$

Step 3

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

$\frac{3 b^{5}}{3 a^{- 2} b^{- 3} a^{5}}$

Step 4

Multiply $a^{- 2}$ by $a^{5}$ by adding the exponents.

Tap for more steps...

Step 4.1

Move $a^{5}$ .

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

Step 4.2

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

$\frac{3 b^{5}}{3 a^{5 - 2} b^{- 3}}$

Step 4.3

Subtract $2$ from $5$ .

$\frac{3 b^{5}}{3 a^{3} b^{- 3}}$

Step 5

Move $b^{- 3}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{3 b^{5} b^{3}}{3 a^{3}}$

Step 6

Multiply $b^{5}$ by $b^{3}$ by adding the exponents.

Tap for more steps...

Step 6.1

Move $b^{3}$ .

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

Step 6.2

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

$\frac{3 b^{3 + 5}}{3 a^{3}}$

Step 6.3

Add $3$ and $5$ .

$\frac{3 b^{8}}{3 a^{3}}$

Step 7

Cancel the common factor of $3$ .

Tap for more steps...

Step 7.1

Cancel the common factor.

$\frac{3 b^{8}}{3 a^{3}}$

Step 7.2

Rewrite the expression.

$\frac{b^{8}}{a^{3}}$