Simplify (6^-2)(3^-3)(3*6)^4

$(6^{- 2}) (3^{- 3}) {(3 \cdot 6)}^{4}$

Step 1

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

$\frac{1}{6^{2}} \cdot 3^{- 3} {(3 \cdot 6)}^{4}$

Step 2

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

$\frac{1}{36} \cdot 3^{- 3} {(3 \cdot 6)}^{4}$

Step 3

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

$\frac{1}{36} \cdot \frac{1}{3^{3}} {(3 \cdot 6)}^{4}$

Step 4

Combine.

$\frac{1 \cdot 1}{36 \cdot 3^{3}} {(3 \cdot 6)}^{4}$

Step 5

Simplify the expression.

Multiply $1$ by $1$ .

$\frac{1}{36 \cdot 3^{3}} {(3 \cdot 6)}^{4}$

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

$\frac{1}{36 \cdot 27} {(3 \cdot 6)}^{4}$

Multiply $36$ by $27$ .

$\frac{1}{972} {(3 \cdot 6)}^{4}$

Multiply $3$ by $6$ .

$\frac{1}{972} \cdot 18^{4}$

Raise $18$ to the power of $4$ .

$\frac{1}{972} \cdot 104976$

Step 6

Cancel the common factor of $972$ .

Factor $972$ out of $104976$ .

$\frac{1}{972} \cdot (972 (108))$

Cancel the common factor.

$\frac{1}{972} \cdot (972 \cdot 108)$

Rewrite the expression.

$108$