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Integrated Math II
21. CC.HSN.RN.A.1
21.4 Exponents: Power rule: (a^x)^y = a^(xy)
Power Rule for Exponents
See exactly how the power rule for exponents works, why raising a power to another power means multiplying exponents, and how to apply it step by step.
What You'll Learn
The power rule for exponents states that a power raised to another power is found by multiplying the exponents together
This works because raising a power to another power means multiplying repeated copies of the same base
The rule applies the same way with negative or variable exponents, as long as the base stays the same
The power rule is one of several exponent laws, and combining it with the product and quotient rules lets you simplify more complex expressions
Careful bracket placement matters, since only the exponent directly attached to the base gets multiplied
What You'll Practice
1
Proving the power rule by expanding expressions and counting factors
2
Applying the power rule to expressions with multiple variables and exponents
3
Simplifying complex fractions with exponents raised to powers
4
Working with negative and positive exponents in power rule problems
Why This Matters
The power rule is essential for simplifying complex expressions throughout algebra, calculus, and beyond. You'll use this property constantly when working with polynomials, exponential functions, scientific notation, and advanced math courses.
Before You Start — Make Sure You Can:
This Unit Includes
3 Video lessons
Practice exercises
Learning resources
Skills
Power Rule
Exponent Laws
Simplification
Algebra
Exponential Expressions
Multiplication of Exponents
OH Curriculum Aligned