Simplify (6z^8)/(-2(z^-3)^5)

$\frac{6 z^{8}}{- 2 {(z^{- 3})}^{5}}$

Step 1

Cancel the common factor of $6$ and $- 2$ .

Factor $2$ out of $6 z^{8}$ .

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

Cancel the common factors.

Factor $2$ out of $- 2 {(z^{- 3})}^{5}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 2

Simplify the denominator.

Multiply the exponents in ${(z^{- 3})}^{5}$ .

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

$\frac{3 z^{8}}{- z^{- 3 \cdot 5}}$

Multiply $- 3$ by $5$ .

$\frac{3 z^{8}}{- z^{- 15}}$

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

$\frac{3 z^{8}}{- \frac{1}{z^{15}}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$3 z^{8} (- z^{15})$

Step 4

Rewrite using the commutative property of multiplication.

$3 \cdot - 1 z^{8} z^{15}$

Step 5

Multiply $z^{8}$ by $z^{15}$ by adding the exponents.

Move $z^{15}$ .

$3 \cdot - 1 (z^{15} z^{8})$

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

$3 \cdot - 1 z^{15 + 8}$

Add $15$ and $8$ .

$3 \cdot - 1 z^{23}$

Step 6

Multiply $3$ by $- 1$ .

$- 3 z^{23}$