Base (in Exponents)
High School
Definition
In exponential expressions, the base is the number that is being multiplied by the exponent or power. For example, in \(2^3\), 2 is the base while 3 is the exponent or power.
Worked examples
\(5^4 = 5 \times 5 \times 5 \times 5 = 625\)
The base 5 is multiplied by itself 4 times because the exponent is 4.
\((-3)^2 = (-3) \times (-3) = 9\)
The base is -3 (including the negative sign inside parentheses), so it is squared.
\(x^5\)
The base can be a variable; here x is multiplied by itself 5 times.
Common mistakes
- \(-3^2 = 9\) → \(-3^2 = -9\) Without parentheses, the base is 3, not -3, so only 3 is squared and the negative stays outside.
- In \(2^3\), 3 is the base → In \(2^3\), 2 is the base The base is the number being multiplied repeatedly; 3 is the exponent.
- \(4 \cdot 3^2 = 12^2 = 144\) → \(4 \cdot 3^2 = 4 \cdot 9 = 36\) The base is only 3, not 4·3. Exponents apply before multiplication.
Where you'll use it next
Understanding the base is essential when you simplify exponential expressions, apply exponent rules, solve exponential equations, and work with scientific notation and logarithms in algebra and beyond.
Found in 1 StudyPug lesson
Understanding Exponents: From Basics to Advanced Concepts
7th Grade7thGrade 7 Math
Dive into the world of exponents! Learn fundamental rules, tackle common mistakes, and explore real-world applications. Perfect for students seeking to enhance their math skills and problem-solving abilities.
See also
Reviewed by Pat Cheng, M.Ed. — StudyPug Curriculum Lead · Last updated June 6, 2026