Evaluate (7+3^2)/(4^2*2)

$\frac{7 + 3^{2}}{4^{2} \cdot 2}$

Simplify the numerator.

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

$\frac{7 + 9}{4^{2} \cdot 2}$

Add $7$ and $9$ .

$\frac{16}{4^{2} \cdot 2}$

Simplify the denominator.

Rewrite $4$ as $2^{2}$ .

$\frac{16}{{(2^{2})}^{2} \cdot 2}$

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

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

$\frac{16}{2^{2 \cdot 2} \cdot 2}$

Multiply $2$ by $2$ .

$\frac{16}{2^{4} \cdot 2}$

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

$\frac{16}{2^{4 + 1}}$

Add $4$ and $1$ .

$\frac{16}{2^{5}}$

Reduce the expression by cancelling the common factors.

Raise $2$ to the power of $5$ .

$\frac{16}{32}$

Cancel the common factor of $16$ and $32$ .

Factor $16$ out of $16$ .

$\frac{16 (1)}{32}$

Cancel the common factors.

Factor $16$ out of $32$ .

$\frac{16 \cdot 1}{16 \cdot 2}$

Cancel the common factor.

$\frac{16 \cdot 1}{16 \cdot 2}$

Rewrite the expression.

$\frac{1}{2}$

The result can be shown in multiple forms.

Exact Form:

$\frac{1}{2}$

Decimal Form:

$0.5$