Simplify (-5cd^-4)(2cd^2)^2

$(- 5 c d^{- 4}) {(2 c d^{2})}^{2}$

Step 1

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

$- 5 c \frac{1}{d^{4}} {(2 c d^{2})}^{2}$

Step 2

Multiply $- 5 c \frac{1}{d^{4}}$ .

Combine $- 5$ and $\frac{1}{d^{4}}$ .

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

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

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

Step 3

Simplify the expression.

Move $- 5$ to the left of $c$ .

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

Move the negative in front of the fraction.

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

Step 4

Multiply $5$ by $c$ .

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

Step 5

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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

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

Apply the product rule to $2 c$ .

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

Step 6

Simplify the expression.

Raise $2$ to the power of $2$ .

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

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

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

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

Multiply $2$ by $2$ .

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

Step 7

Cancel the common factor of $d^{4}$ .

Move the leading negative in $- \frac{5 c}{d^{4}}$ into the numerator.

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

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

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

Cancel the common factor.

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

Rewrite the expression.

$- 5 c (4 c^{2})$

Step 8

Multiply $4$ by $- 5$ .

$- 20 c \cdot c^{2}$

Step 9

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

Move $c^{2}$ .

$- 20 (c^{2} c)$

Multiply $c^{2}$ by $c$ .

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

$- 20 (c^{2} c^{1})$

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

$- 20 c^{2 + 1}$

Add $2$ and $1$ .

$- 20 c^{3}$

Simplify (-5cd^-4)(2cd^2)^2

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