According to the order of operations, expressions inside parentheses are evaluated first, followed by exponents, then multiplication and division from left to right, and finally addition and subtraction are evaluated last. We can use the acronym PEMDAS to help us remember the correct order!
For the given expression, this means evaluating the expression inside the parentheses completely before adding the product.
4^3-1/2(7^2+5)
Notice also that even within this parenthetical expression, we must follow the order of operations.
4^3-1/2(54)
Let's do it!
Operation
Before Simplification
After Simplification
Calculate power
4^3-1/2(54)
64-1/2(54)
Multiply
64- 1/2( 54)
64- 54/2
Divide
64-54/2
64- 27
Subtract term
64- 27
37
The expression is equal to 37.
Alternative Solution
Using a Calculator
We can also evaluate this expression using a calculator. To do so, we type it as shown below.
Whenever using a calculator for a complicated expression such as this, be very careful when placing the parentheses. A calculator will only do what it is told to do, not what you meant for it do.
