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Overview
Foundations of Mathematics and Pre-Calculus 10
1. Operations on powers with integral exponents
1.15 Exponents: Zero exponent: a^0 = 1
Zero Exponent Rule
Discover why any nonzero number raised to the power of zero always equals 1, and practice applying the rule correctly.
What You'll Learn
The zero exponent rule states that any nonzero number raised to the power of zero equals 1, written as a to the power 0 equals 1
The rule comes from dividing a power by itself, such as a to the third divided by a to the third, which simplifies to both a to the zero and to 1
The base can be a number, a variable, or an entire expression, as long as it is not equal to zero
Zero raised to the power of zero is considered undefined, so the rule only applies when the base is nonzero
Multiplying a zero exponent term by other exponent terms leaves the rest of the expression unchanged, since the zero exponent term equals 1
What You'll Practice
1
Proving that specific numbers to the zero power equal 1
2
Simplifying expressions using the zero exponent rule
3
Applying multiplication and negative exponent laws in proofs
Why This Matters
Understanding the zero exponent rule is essential for algebra and beyond. You'll use this rule constantly when simplifying expressions, solving equations, and working with scientific notation in chemistry and physics.
Before You Start — Make Sure You Can:
This Unit Includes
1 Video lesson
Practice exercises
Learning resources
Skills
Exponents
Zero Exponent Rule
Exponent Laws
Multiplication Law
Negative Exponents
Mathematical Proof
BC Curriculum Aligned