Algebra Examples

$\frac{8^{- 1} a^{- 2} b^{- 3}}{24^{- 1} a^{- 4} b^{0}}$

Step 1

Move $8^{- 1}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{a^{- 2} b^{- 3}}{24^{- 1} a^{- 4} b^{0} \cdot 8}$

Step 2

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

$\frac{a^{- 2}}{24^{- 1} a^{- 4} b^{0} \cdot 8 b^{3}}$

Step 3

Multiply $b^{0}$ by $b^{3}$ by adding the exponents.

Tap for more steps...

Step 3.1

Move $b^{3}$ .

$\frac{a^{- 2}}{24^{- 1} a^{- 4} (b^{3} b^{0}) \cdot 8}$

Step 3.2

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

$\frac{a^{- 2}}{24^{- 1} a^{- 4} b^{3 + 0} \cdot 8}$

Step 3.3

Add $3$ and $0$ .

$\frac{a^{- 2}}{24^{- 1} a^{- 4} b^{3} \cdot 8}$

Step 4

Move $a^{- 4}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{a^{- 2} a^{4}}{24^{- 1} b^{3} \cdot 8}$

Step 5

Move $24^{- 1}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{a^{- 2} a^{4} \cdot 24}{b^{3} \cdot 8}$

Step 6

Multiply $a^{- 2}$ by $a^{4}$ by adding the exponents.

Tap for more steps...

Step 6.1

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

$\frac{a^{- 2 + 4} \cdot 24}{b^{3} \cdot 8}$

Step 6.2

Add $- 2$ and $4$ .

$\frac{a^{2} \cdot 24}{b^{3} \cdot 8}$

Step 7

Cancel the common factor of $24$ and $8$ .

Tap for more steps...

Step 7.1

Factor $8$ out of $a^{2} \cdot 24$ .

$\frac{8 (a^{2} \cdot 3)}{b^{3} \cdot 8}$

Step 7.2

Cancel the common factors.

Tap for more steps...

Step 7.2.1

Factor $8$ out of $b^{3} \cdot 8$ .

$\frac{8 (a^{2} \cdot 3)}{8 \cdot b^{3}}$

Step 7.2.2

Cancel the common factor.

$\frac{8 (a^{2} \cdot 3)}{8 \cdot b^{3}}$

Step 7.2.3

Rewrite the expression.

$\frac{a^{2} \cdot 3}{b^{3}}$

Step 8

Move $3$ to the left of $a^{2}$ .

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