Write the Fraction in Simplest Form (20z^-9)/((-5z)^2)

$\frac{20 z^{- 9}}{{(- 5 z)}^{2}}$

Step 1

Move $z^{- 9}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{20}{{(- 5 z)}^{2} z^{9}}$

Step 2

Simplify the denominator.

Apply the product rule to $- 5 z$ .

$\frac{20}{{(- 5)}^{2} z^{2} z^{9}}$

Multiply $z^{2}$ by $z^{9}$ by adding the exponents.

Move $z^{9}$ .

$\frac{20}{{(- 5)}^{2} (z^{9} z^{2})}$

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

$\frac{20}{{(- 5)}^{2} z^{9 + 2}}$

Add $9$ and $2$ .

$\frac{20}{{(- 5)}^{2} z^{11}}$

Raise $- 5$ to the power of $2$ .

$\frac{20}{25 z^{11}}$

Step 3

Cancel the common factor of $20$ and $25$ .

Factor $5$ out of $20$ .

$\frac{5 (4)}{25 z^{11}}$

Cancel the common factors.

Factor $5$ out of $25 z^{11}$ .

$\frac{5 (4)}{5 (5 z^{11})}$

Cancel the common factor.

$\frac{5 \cdot 4}{5 (5 z^{11})}$

Rewrite the expression.

$\frac{4}{5 z^{11}}$