Order Of Operations With Exponents
Introduction for order of operations with exponents:
Order of operation is very basic knowledge about how to calculate an arithmetic expression. Order of operation has some rules about how to solve an arithmetic expression. Here Order of operation is also called as PEMDAS. Each letter have its own meaning. Order of operation involves arithmetic operations and parenthesis, exponents. Arithmetic operations are addition(+), subtraction(-), multiplication(*) and division().
PEMDAS - Each letter stands for P-Paranthesis, E-Exponents,M-Multiplication,D-Division, A-Addition, S-Subtraction.
Steps for Solving Rorder of Operations with Exponents
The following steps are used to solve arithmetic expression by using order of operations.
Step 1: First Solve the arithmetic operation inside parenthesis.
Step 2: Then solve the exponents operation.
Step 3: Then solve the multiplication and division operation from left to right order.
Step 4: Then solve the addition and subtraction operation from left to right order.
Let us solve the problems on order of operations with exponents.
Example Problems for Order of Operations with Exponents:
Problem 1: Solve the arithmetic expression 32 x 43 using order of operations.
Sol : There is no parenthesis so we go to next operation.
Exponents are here. So we have to calculate each exponent operation.
32 = 3 x 3 = 9
43 = 4 x 4 x 4 = 64
So the expression is reduced to 9 x 64 .
Then we go to next operation.
Multiplication of these two numbers are 9 x 64 = 576.
The answer is 576 .
Problem 2: Solve the arithmetic expression: 27 - 256 43 using order of operations.
Sol : There is no parenthesis so we go to next operation.
Exponent is going to calculate.
43 = 4 x 4 x 4 = 64
So the expression is reduced to 27 - 256 64
Now we are going to solve division operation.
256 64 = 4
So the expression is reduced to 27 - 4.
We are going to solve subtraction operation.
27 - 4 = 23
The answer is 23.
Problem 3: Solve the arithmetic expression: 9 x (5 + 3)2 - 144 using order of operations.
Sol : First we solve the addition operation inside parenthesis.
5 + 3 = 8 .
So the expression is reduced to 9 x 82 - 144
We are going to solve exponent operation.
82 = 8 x 8 = 64
So the expression is reduced to 9 x 64 - 144.
We are going to solve multiplication operation.
9 x 64 = 576
So the expression is reduced to 576 - 144
We are going to solve subtraction operation.
576 - 144 = 432 .
The answer is 432 .
Problem 4: Steven charges $20 per square foot to lay a floor. If a square-shaped hallway is 9 feet along one side, and the customer has a coupon for $30 off the total, then how much will the floor cost?
Sol : If one side of hallway is 9 feet then area of the hallway is (9 feet)2 .
The arithmetic expression is
$20 x 92 - $30
using order of operations,
We are going to solve exponent operation.
92 = 9 x 9 = 81
So the expression is reduced to $20 x 81 - $30
We are going to solve multiplication operation.
$20 x 81 = $ 1620
So the expression is reduced to $ 1620 - $30
We are going to solve subtraction operation.
$ 1620 - $ 30 = $ 1590
The cost of floor is $ 1590 .
by: Omkar Nayak
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