Evaluate ((-6)^-5)/(3^-2)

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

Step 1

Simplify the expression.

Move ${(- 6)}^{- 5}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{1}{3^{- 2} {(- 6)}^{5}}$

Move $3^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

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

Raise $3$ to the power of $2$ .

$\frac{9}{{(- 6)}^{5}}$

Raise $- 6$ to the power of $5$ .

$\frac{9}{- 7776}$

Step 2

Cancel the common factor of $9$ and $- 7776$ .

Factor $9$ out of $9$ .

$\frac{9 (1)}{- 7776}$

Cancel the common factors.

Factor $9$ out of $- 7776$ .

$\frac{9 \cdot 1}{9 \cdot - 864}$

Cancel the common factor.

$\frac{9 \cdot 1}{9 \cdot - 864}$

Rewrite the expression.

$\frac{1}{- 864}$

Step 3

Move the negative in front of the fraction.

$- \frac{1}{864}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$- \frac{1}{864}$

Decimal Form:

$- 0.00115740 \dots$