Order of Operations: (Exponents) - Examples, Exercises and Solutions

Understanding Order of Operations: (Exponents)

Complete explanation with examples

As part of combined operations, we learned that parentheses always come first.

Once solved, we can begin to simplify powers (or roots).

After simplifying them, we can continue solving the exercise according to the order of basic operations:

Firstly, the multiplications and divisions, and lastly, the additions and subtractions.

Let's refresh the order of operations:

  1. Parentheses
  2. Powers and roots
  3. Multiplications and divisions
  4. Additions and subtractions
Detailed explanation of the BODMAS/PEMDAS rule highlighting 'Order' (Exponents) with symbols like √x and x², crucial for solving complex arithmetic expressions step by step.

Detailed explanation

Practice Order of Operations: (Exponents)

Test your knowledge with 24 quizzes

\( 10:2-2^2= \)

Examples with solutions for Order of Operations: (Exponents)

Step-by-step solutions included
Exercise #1

20−33:3= 20-3^3:3=

Step-by-Step Solution

First, compute the power: 33=27 3^3 = 27 .

Next, divide: 27÷3=9 27 \div 3 = 9 .

Finally, subtract: 20−9=11 20 - 9 = 11 .

Answer:

11 11

Exercise #2

15−42:2= 15-4^2:2=

Step-by-Step Solution

First, compute the power: 42=16 4^2 = 16 .

Next, divide: 16÷2=8 16 \div 2 = 8 .

Finally, subtract: 15−8=7 15 - 8 = 7 .

Answer:

7 7

Exercise #3

10−52:5= 10-5^2:5=

Step-by-Step Solution

First, compute the power: 52=25 5^2 = 25 .

Next, divide: 25÷5=5 25 \div 5 = 5 .

Finally, subtract: 10−5=5 10 - 5 = 5 .

Answer:

5 5

Exercise #4

8−16×3= 8 - \sqrt{16} \times 3 =

Step-by-Step Solution

First, evaluate the square root: 16=4\sqrt{16}=4.

Then, follow the order of operations (PEMDAS/BODMAS):

1. Multiplication: 4×3=124 \times 3 = 12

2. Subtraction: 8−12=−48 - 12 = -4

So, the correct answer is −4 -4 .

Answer:

−4 -4

Exercise #5

7+49−5= 7 + \sqrt{49} - 5 =

Step-by-Step Solution

First, evaluate the square root: 49=7\sqrt{49}=7.

Then, follow the order of operations (PEMDAS/BODMAS):

1. Addition: 7+7=147 + 7 = 14

2. Subtraction: 14−5=914 - 5 = 9

So, the correct answer is 9 9 .

Answer:

9 9

More Order of Operations: (Exponents) Questions

Click on any question to see the complete solution with step-by-step explanations

Powers and Roots

Calculate (2/3)³: Finding the Cube of a Fraction Solve: 6 + Square Root of 64 - 4 Expression Evaluation Solve 18² - (100 + √9): Mixed Operations Expression Solve 2×(√36 + 9): Order of Operations with Square Root Solve 2×(3³ + √144): Order of Operations Practice

Continue Your Math Journey

Master Order of Operations: (Exponents) first, then advance to these related topics that build on your fraction skills

Suggested Topics to Practice in Advance

The Order of Basic Operations: Addition, Subtraction, and Multiplication

Topics Learned in Later Sections

Order of Operations: RootsOrder of Operations - Exponents and RootsOrder of Operations with ParenthesesDivision and Fraction Bars (Vinculum)The Numbers 0 and 1 in OperationsNeutral Element (Identity Element)Order or Hierarchy of Operations with FractionsMultiplicative InverseSpecial cases (0 and 1, reciprocals, fraction line)The Order of Operations

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