Answer
$\frac{55}{8}$
Work Step by Step
The order of operations states that first we perform operations inside grouping symbols, such as parentheses, brackets, and fraction bars. Then, we simplify powers. Then, we multiply and divide from left to right. Finally, we add and subtract from left to right. We use these rules to simplify the expression.
Start with the given expression: $\frac{22+1^3+(3^4-7^2)}{2^3}$
Since we have multiple layers of grouping (fraction bar and parentheses) we start with the inner most grouping and simplify on the inside of the parentheses:
We simplify the exponents first: $\frac{22+1^3+(81-49)}{2^3}$
Then, we subtract inside the parentheses: $\frac{22+1^3+32}{2^3}$
Next, we simplify the numerator, which is above the fraction bar:
We simplify the exponents: $\frac{22+1+32}{2^3}$
We add from left to right: $\frac{23+32}{2^3}=\frac{55}{2^3}$
We simplify the denominator by simplify the power: $\frac{55}{8}$
