Simplify (4(z)^2)/(-20z^-6)

$\frac{4 {(z)}^{2}}{- 20 z^{- 6}}$

Step 1

Move $z^{- 6}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{4 {(z)}^{2} z^{6}}{- 20}$

Step 2

Multiply ${(z)}^{2}$ by $z^{6}$ by adding the exponents.

Move $z^{6}$ .

$\frac{4 (z^{6} {(z)}^{2})}{- 20}$

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

$\frac{4 z^{6 + 2}}{- 20}$

Add $6$ and $2$ .

$\frac{4 z^{8}}{- 20}$

Step 3

Cancel the common factor of $4$ and $- 20$ .

Factor $4$ out of $4 z^{8}$ .

$\frac{4 (z^{8})}{- 20}$

Cancel the common factors.

Factor $4$ out of $- 20$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

Move the negative in front of the fraction.

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