Simplify 4c^8d^-3*5c^-5d^-1

$4 c^{8} d^{- 3} \cdot 5 c^{- 5} d^{- 1}$

Step 1

Multiply $c^{8}$ by $c^{- 5}$ by adding the exponents.

Move $c^{- 5}$ .

$4 (c^{- 5} c^{8}) d^{- 3} \cdot (5 d^{- 1})$

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

$4 c^{- 5 + 8} d^{- 3} \cdot (5 d^{- 1})$

Add $- 5$ and $8$ .

$4 c^{3} d^{- 3} \cdot (5 d^{- 1})$

Step 2

Multiply $d^{- 3}$ by $d^{- 1}$ by adding the exponents.

Move $d^{- 1}$ .

$4 c^{3} (d^{- 1} d^{- 3}) \cdot 5$

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

$4 c^{3} d^{- 1 - 3} \cdot 5$

Subtract $3$ from $- 1$ .

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

Step 3

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

$4 c^{3} \frac{1}{d^{4}} \cdot 5$

Step 4

Multiply $4 c^{3} \frac{1}{d^{4}}$ .

Combine $4$ and $\frac{1}{d^{4}}$ .

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

Combine $c^{3}$ and $\frac{4}{d^{4}}$ .

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

Step 5

Move $4$ to the left of $c^{3}$ .

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

Step 6

Multiply $\frac{4 c^{3}}{d^{4}} \cdot 5$ .

Combine $\frac{4 c^{3}}{d^{4}}$ and $5$ .

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

Multiply $5$ by $4$ .

$\frac{20 c^{3}}{d^{4}}$