Simplify (3^-3)/(6^-2)

$\frac{3^{- 3}}{6^{- 2}}$

Step 1

Simplify the expression.

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

$\frac{1}{6^{- 2} \cdot 3^{3}}$

Move $6^{- 2}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{6^{2}}{3^{3}}$

Raise $6$ to the power of $2$ .

$\frac{36}{3^{3}}$

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

$\frac{36}{27}$

Step 2

Cancel the common factor of $36$ and $27$ .

Factor $9$ out of $36$ .

$\frac{9 (4)}{27}$

Cancel the common factors.

Factor $9$ out of $27$ .

$\frac{9 \cdot 4}{9 \cdot 3}$

Cancel the common factor.

$\frac{9 \cdot 4}{9 \cdot 3}$

Rewrite the expression.

$\frac{4}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\frac{4}{3}$

Decimal Form:

$1.\overline{3}$

Mixed Number Form:

$1 \frac{1}{3}$