Evaluate (3^-24^2)/(3^04^3)

$\frac{3^{- 2} \cdot 4^{2}}{3^{0} \cdot 4^{3}}$

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

$\frac{4^{2}}{3^{0} \cdot 4^{3} \cdot 3^{2}}$

Multiply $3^{0}$ by $3^{2}$ by adding the exponents.

Move $3^{2}$ .

$\frac{4^{2}}{3^{2} \cdot 3^{0} \cdot 4^{3}}$

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

$\frac{4^{2}}{3^{2 + 0} \cdot 4^{3}}$

Add $2$ and $0$ .

$\frac{4^{2}}{3^{2} \cdot 4^{3}}$

Cancel the common factor of $4^{2}$ and $4^{3}$ .

Multiply by $1$ .

$\frac{4^{2} \cdot 1}{3^{2} \cdot 4^{3}}$

Cancel the common factors.

Factor $4^{2}$ out of $3^{2} \cdot 4^{3}$ .

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

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{3^{2} \cdot 4}$

Simplify the expression.

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

$\frac{1}{9 \cdot 4}$

Multiply $9$ by $4$ .

$\frac{1}{36}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{36}$

Decimal Form:

$0.02\overline{7}$

Evaluate (3^-2*4^2)/(3^0*4^3)