Algebra Examples

$\frac{10 {(c^{2} d^{- 8})}^{3}}{2 c^{- 1} d^{4}}$

Step 1

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 1.1

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

$\frac{10 {(c^{2} d^{- 8})}^{3} c}{2 d^{4}}$

Step 1.2

Cancel the common factor of $10$ and $2$ .

Tap for more steps...

Step 1.2.1

Factor $2$ out of $10 {(c^{2} d^{- 8})}^{3} c$ .

$\frac{2 (5 {(c^{2} d^{- 8})}^{3} c)}{2 d^{4}}$

Step 1.2.2

Cancel the common factors.

Tap for more steps...

Step 1.2.2.1

Factor $2$ out of $2 d^{4}$ .

$\frac{2 (5 {(c^{2} d^{- 8})}^{3} c)}{2 (d^{4})}$

Step 1.2.2.2

Cancel the common factor.

$\frac{2 (5 {(c^{2} d^{- 8})}^{3} c)}{2 d^{4}}$

Step 1.2.2.3

Rewrite the expression.

$\frac{5 {(c^{2} d^{- 8})}^{3} c}{d^{4}}$

Step 2

Simplify the numerator.

Tap for more steps...

Step 2.1

Apply the product rule to $c^{2} d^{- 8}$ .

$\frac{5 {(c^{2})}^{3} {(d^{- 8})}^{3} c}{d^{4}}$

Step 2.2

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

Tap for more steps...

Step 2.2.1

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

$\frac{5 c^{2 \cdot 3} {(d^{- 8})}^{3} c}{d^{4}}$

Step 2.2.2

Multiply $2$ by $3$ .

$\frac{5 c^{6} {(d^{- 8})}^{3} c}{d^{4}}$

Step 2.3

Multiply the exponents in ${(d^{- 8})}^{3}$ .

Tap for more steps...

Step 2.3.1

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

$\frac{5 c^{6} d^{- 8 \cdot 3} c}{d^{4}}$

Step 2.3.2

Multiply $- 8$ by $3$ .

$\frac{5 c^{6} d^{- 24} c}{d^{4}}$

Step 2.4

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

$\frac{5 c^{6} \frac{1}{d^{24}} c}{d^{4}}$

Step 2.5

Combine exponents.

Tap for more steps...

Step 2.5.1

Combine $5$ and $\frac{1}{d^{24}}$ .

$\frac{c^{6} \frac{5}{d^{24}} c}{d^{4}}$

Step 2.5.2

Combine $c^{6}$ and $\frac{5}{d^{24}}$ .

$\frac{\frac{c^{6} \cdot 5}{d^{24}} c}{d^{4}}$

Step 2.5.3

Combine $\frac{c^{6} \cdot 5}{d^{24}}$ and $c$ .

$\frac{\frac{c^{6} \cdot 5 c}{d^{24}}}{d^{4}}$

Step 2.5.4

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

$\frac{\frac{5 (c^{6} c^{1})}{d^{24}}}{d^{4}}$

Step 2.5.5

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

$\frac{\frac{5 c^{6 + 1}}{d^{24}}}{d^{4}}$

Step 2.5.6

Add $6$ and $1$ .

$\frac{\frac{5 c^{7}}{d^{24}}}{d^{4}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$\frac{5 c^{7}}{d^{24}} \cdot \frac{1}{d^{4}}$

Step 4

Combine.

$\frac{5 c^{7} \cdot 1}{d^{24} d^{4}}$

Step 5

Multiply $d^{24}$ by $d^{4}$ by adding the exponents.

Tap for more steps...

Step 5.1

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

$\frac{5 c^{7} \cdot 1}{d^{24 + 4}}$

Step 5.2

Add $24$ and $4$ .

$\frac{5 c^{7} \cdot 1}{d^{28}}$

Step 6

Multiply $5 c^{7}$ by $1$ .

$\frac{5 c^{7}}{d^{28}}$