Read the Notation
In 43, the base is 4 and the exponent is 3. Read it as “four to the third power.”
Free Interactive Pre-Algebra Tool
Exponents, Powers, and Square Roots
Learn what bases and exponents mean, build powers as repeated multiplication, evaluate them step by step, and connect perfect squares with their square roots.
Learn How Powers and Square Roots Work
Review bases, exponents, repeated multiplication, powers of zero and one, perfect squares, square roots, and worked examples.
Read the Exponents and Square Roots GuideHow It Works
Build Meaning Before You Calculate
Exponential notation is a shortcut for repeated multiplication. Square roots reverse the process by asking which nonnegative number was multiplied by itself to make a perfect square.
Expand the Power
Use the exponent to decide how many copies of the base to multiply: 43 = 4 × 4 × 4.
Evaluate Step by Step
Multiply two factors at a time and keep each partial product visible until you reach the value.
Reverse With a Root
Because 7 × 7 = 49, 72 = 49 and the principal square root of 49 is 7.
Interactive Practice
Work Through Each Problem
Correct
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Problems
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Evaluate the Power
MediumBuild the meaning of the expression before finding its value.
34
81
A power tells you how many times to use the base as
a factor.
- 1 Interpret
- 2 Expand
- 3 Evaluate
- 4 Explain
1
Current Step
Interpret the Notation
Identify What the Symbols Mean
Enter the base and exponent shown in the expression.
Choose the multiplication fact that matches the square root.
2
Locked
Show the Structure
Write the Multiplication
Complete Step 1 to unlock the multiplication model.
3
Locked
Calculate Carefully
Find the Value
Complete Step 2 to unlock the calculation.
The exponent tells how many copies of the base belong in the multiplication—not how many times to multiply the base by the exponent.
Step 4 · Explain the Connection
You Built the Entire Solution
Your interpretation, multiplication model, and calculation remain visible above so you can see how each step supports the next.
34 = 3 × 3 × 3 × 3 = 81
The exponent 4 uses four factors of 3. Their product is 81.
Keep This Nearby
Perfect Squares Reference
A perfect square is the product of a whole number multiplied by itself.
12 = 1
22 = 4
32 = 9
42 = 16
52 = 25
62 = 36
72 = 49
82 = 64
92 = 81
102 = 100
112 = 121
122 = 144
132 = 169
142 = 196
152 = 225
Key Reminders
Avoid the Most Common Exponent Mistakes
Keep these relationships in view while you practice.
The Exponent Counts Factors
It tells how many copies of the base are multiplied together.
53 = 5 × 5 × 5
Do Not Multiply Base by Exponent
A power represents repeated multiplication, not ordinary multiplication of its two visible numbers.
53 = 125, not 15
A Square Root Reverses Squaring
Find the nonnegative number whose square equals the number inside the radical.
√64 = 8 because 82 = 64
Zero and One Are Special
Any nonzero base to the zero power is 1, and every power of 1 remains 1.
90 = 1 and 19 = 1
Keep Learning
Understand Why Powers and Roots Work
Review exponent vocabulary, repeated multiplication, squares, cubes, special powers, perfect squares, square roots, and fully worked examples in the complete guide.
Read the Exponents and Roots Guide