According to the order of operations, expressions inside parentheses are evaluated first, while addition and subtraction are evaluated last. For the given expression, this means evaluating completely the expressions inside the numerator and the denominator before calculating the fraction.
22+1^3+(3^4 - 7^2)/2^3Notice also that even within the numerator, we must obey the order of operations.
22+1^3+(3^4 - 7^2)
For this, we must remember to evaluate the exponents first, the difference inside parentheses next, and finally, the sum of the resulting terms.
Operation
Before Simplification
After Simplification
Calculate power
22+ 1^3+( 3^4 - 7^2)/2^3
22+ 1+( 81 - 49)/8
Subtract term
22+1+( 81 - 49)/8
22+1+ 32/8
Add terms
22+ 1+32/8
23 + 32/8
Add terms
23 + 32/8
55/8
Calculate quotient
55/8
6.875
The expression equals 6.875.
Alternative Solution
Using a Calculator
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