Simplify (3^3)(4^0)^2(3*2)^-3(2^2)

$(3^{3}) {(4^{0})}^{2} {(3 \cdot 2)}^{- 3} (2^{2})$

Step 1

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

$27 {(4^{0})}^{2} {(3 \cdot 2)}^{- 3} \cdot 2^{2}$

Step 2

Multiply the exponents in ${(4^{0})}^{2}$ .

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

$27 \cdot 4^{0 \cdot 2} {(3 \cdot 2)}^{- 3} \cdot 2^{2}$

Multiply $0$ by $2$ .

$27 \cdot 4^{0} {(3 \cdot 2)}^{- 3} \cdot 2^{2}$

Step 3

Anything raised to $0$ is $1$ .

$27 \cdot 1 {(3 \cdot 2)}^{- 3} \cdot 2^{2}$

Step 4

Multiply $27$ by $1$ .

$27 {(3 \cdot 2)}^{- 3} \cdot 2^{2}$

Step 5

Multiply $3$ by $2$ .

$27 \cdot 6^{- 3} \cdot 2^{2}$

Step 6

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

$27 \cdot \frac{1}{6^{3}} \cdot 2^{2}$

Step 7

Raise $6$ to the power of $3$ .

$27 \cdot \frac{1}{216} \cdot 2^{2}$

Step 8

Cancel the common factor of $27$ .

Factor $27$ out of $216$ .

$27 \cdot \frac{1}{27 (8)} \cdot 2^{2}$

Cancel the common factor.

$27 \cdot \frac{1}{27 \cdot 8} \cdot 2^{2}$

Rewrite the expression.

$\frac{1}{8} \cdot 2^{2}$

Step 9

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

$\frac{1}{8} \cdot 4$

Step 10

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

$\frac{1}{4 (2)} \cdot 4$

Cancel the common factor.

$\frac{1}{4 \cdot 2} \cdot 4$

Rewrite the expression.

$\frac{1}{2}$

Step 11

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$

Simplify (3^3)(4^0)^2(3*2)^-3(2^2)

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