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Pre-Algebra · Quick Reference
Exponents Cheat Sheet
In one line: an exponent tells you how many times to multiply a number by itself — a compact way to write repeated multiplication.
Key Ideas
1Base and Exponent. In x^n, x is the base (the number being multiplied) and n is the exponent (how many times to multiply it).
2Exponent of 1 and 0. Any number to the power of 1 equals itself: x^1 = x. Any nonzero number to the power of 0 equals 1: x^0 = 1.
3Product Rule. When multiplying powers with the same base, add the exponents: x^a * x^b = x^(a+b).
4Quotient Rule. When dividing powers with the same base, subtract the exponents: x^a / x^b = x^(a-b).
5Power of a Power Rule. When raising a power to another power, multiply the exponents: (x^a)^b = x^(a*b).
Worked Examples
Evaluate 2^4.
16
Simplify x^3 * x^5.
x^8
Simplify (x^2)^4.
x^8
Formulas
x^a * x^b = x^(a+b)
x^a / x^b = x^(a-b)
(x^a)^b = x^(a*b)
x^(-n) = 1/(x^n)
Practice Yourself
Evaluate 3^2.
9
Evaluate 5^0.
1
Simplify x^4 * x^2.
x^6