Simplify -4w^-3z^-5(8w)^2

$- 4 w^{- 3} z^{- 5} {(8 w)}^{2}$

Step 1

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

$- 4 \frac{1}{w^{3}} z^{- 5} {(8 w)}^{2}$

Step 2

Combine $- 4$ and $\frac{1}{w^{3}}$ .

$\frac{- 4}{w^{3}} z^{- 5} {(8 w)}^{2}$

Step 3

Move the negative in front of the fraction.

$- \frac{4}{w^{3}} z^{- 5} {(8 w)}^{2}$

Step 4

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

$- \frac{4}{w^{3}} \cdot \frac{1}{z^{5}} {(8 w)}^{2}$

Step 5

Multiply $\frac{1}{z^{5}}$ by $\frac{4}{w^{3}}$ .

$- \frac{4}{z^{5} w^{3}} {(8 w)}^{2}$

Step 6

Apply the product rule to $8 w$ .

$- \frac{4}{z^{5} w^{3}} (8^{2} w^{2})$

Step 7

Cancel the common factor of $w^{2}$ .

Move the leading negative in $- \frac{4}{z^{5} w^{3}}$ into the numerator.

$\frac{- 4}{z^{5} w^{3}} (8^{2} w^{2})$

Factor $w^{2}$ out of $z^{5} w^{3}$ .

$\frac{- 4}{w^{2} (z^{5} w)} (8^{2} w^{2})$

Factor $w^{2}$ out of $8^{2} w^{2}$ .

$\frac{- 4}{w^{2} (z^{5} w)} (w^{2} \cdot 8^{2})$

Cancel the common factor.

$\frac{- 4}{w^{2} (z^{5} w)} (w^{2} \cdot 8^{2})$

Rewrite the expression.

$\frac{- 4}{z^{5} w} \cdot 8^{2}$

Step 8

Combine $\frac{- 4}{z^{5} w}$ and $8^{2}$ .

$\frac{- 4 \cdot 8^{2}}{z^{5} w}$

Step 9

Factor out negative.

$\frac{- (4 \cdot 8^{2})}{z^{5} w}$

Step 10

Simplify the expression.

Rewrite $4$ as $2^{2}$ .

$\frac{- (2^{2} \cdot 8^{2})}{z^{5} w}$

Rewrite $8$ as $2^{3}$ .

$\frac{- (2^{2} \cdot {(2^{3})}^{2})}{z^{5} w}$

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

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

$\frac{- (2^{2} \cdot 2^{3 \cdot 2})}{z^{5} w}$

Multiply $3$ by $2$ .

$\frac{- (2^{2} \cdot 2^{6})}{z^{5} w}$

Step 11

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

$\frac{- 2^{2 + 6}}{z^{5} w}$

Step 12

Add $2$ and $6$ .

$\frac{- 2^{8}}{z^{5} w}$

Step 13

Raise $2$ to the power of $8$ .

$\frac{- 1 \cdot 256}{z^{5} w}$

Step 14

Multiply $- 1$ by $256$ .

$\frac{- 256}{z^{5} w}$

Step 15

Move the negative in front of the fraction.

$- \frac{256}{z^{5} w}$

Simplify -4w^-3z^-5(8w)^2

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