Powers and Roots
Powers (indices) provide a shorthand for repeated multiplication, such as 2^4 = 2 x 2 x 2 x 2 = 16. Square roots are the inverse operation: the square root of 16 is 4 because 4 x 4 = 16.
What You Need to Know
Key Concept Diagram
A power (index) indicates repeated multiplication: a^n means a multiplied by itself n times
The square of a number is that number multiplied by itself: 5^2 = 25
The square root (sqrt) is the inverse of squaring: sqrt(25) = 5
Cube numbers: 2^3 = 8, 3^3 = 27, 4^3 = 64
Any number to the power of 0 equals 1: a^0 = 1 (for a not equal to 0)
Key Vocabulary
Index (Power)
The small raised number that tells you how many times to multiply the base by itself
Base
The number being multiplied in a power expression; in 3^4 the base is 3
Square Root
A number that when multiplied by itself gives the original number; sqrt(36) = 6
Cube
A number raised to the power of 3; 4^3 = 4 x 4 x 4 = 64
Knowledge Check
Select the correct answer for each question. Click "Check Answer" to see if you are right.
Question 1
What is the value of 3^4?
Question 2
What is the square root of 144?
Question 3
Evaluate 2^5
Key Concepts Summary
- ●A power (index) indicates repeated multiplication: a^n means a multiplied by itself n times
- ●The square of a number is that number multiplied by itself: 5^2 = 25
- ●The square root (sqrt) is the inverse of squaring: sqrt(25) = 5
- ●Cube numbers: 2^3 = 8, 3^3 = 27, 4^3 = 64
- ●Any number to the power of 0 equals 1: a^0 = 1 (for a not equal to 0)