According to the order of operations, expressions inside parentheses and other grouping symbols are evaluated first, while addition and subtraction are evaluated last. For the given expression, this means evaluating completely the expression inside the numerator before calculating the fraction.
2[8+(67-2^6)^3 ]/9Notice that we must obey the order of operations in the numerator by evaluating the parenthetical expression first.
67-2^6
For this, we must remember to evaluate the exponent first and the difference next.
Operation
Before Simplification
After Simplification
Calculate power
2[8+(67- 2^6)^3 ]/9
2[8+(67- 64)^3 ]/9
Subtract term
2[8+( 67- 64)^3 ]/9
2[8+ 3^3 ]/9
Calculate power
2[8+ 3^3 ]/9
2[8+ 27 ]/9
Add terms
2[ 8+ 27 ]/9
2[ 35]/9
Multiply
2[ 35]/9
70/9
Calculate quotient
70/9
7.777777...
The expression equals about 7.78 or 709.
Alternative Solution
Using a Calculator
We can also evaluate this expression using a calculator. To do so, type it as shown below.
