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Integrated Math II
21. CC.HSN.RN.A.1
21.3 Exponents: Division rule: a^x / a^y = a^(x-y)
Exponents Division Rule: Dividing Powers with the Same Base
Learn how the quotient rule for exponents lets you divide powers with the same base by simply subtracting exponents.
What You'll Learn
The division rule for exponents states that a to the x divided by a to the y equals a to the power of x minus y, as long as the base a is not zero.
The rule only applies when the bases being divided are identical.
Subtracting exponents can produce a negative exponent, which can be rewritten using the negative exponent rule.
Expanding the powers as repeated factors and cancelling shows exactly why the rule works.
This rule is often combined with the product rule and power rules when simplifying larger expressions.
What You'll Practice
1
Simplifying single-variable expressions using the division rule
2
Working with multi-variable expressions involving numbers and multiple bases
3
Subtracting exponents including negative results
4
Proving exponent division properties by expanding powers
Why This Matters
Mastering the division rule for exponents is essential for algebra, calculus, and scientific notation. You'll use this rule constantly when simplifying complex expressions, solving exponential equations, and working with polynomial fractions throughout higher math.
Before You Start — Make Sure You Can:
This Unit Includes
2 Video lessons
Practice exercises
Learning resources
Skills
Exponent Rules
Division of Powers
Simplification
Algebra
Exponent Laws
Polynomial Division
OH Curriculum Aligned