Exponent Rules
Track the base and operation first; then choose the one exponent rule that applies.
Exponent Rules
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Identify the operation before changing any exponent
Exponent rules describe repeated multiplication. They apply only when the required bases and operations match.
Products add exponents, quotients subtract, and powers of powers multiply. These rules do not turn sums such as x²+x³ into one power.
Same base
Product: add; quotient: subtract.
Special exponents
a⁰=1 and a⁻ⁿ=1aⁿ for a≠0.
Read the operation before touching the exponents
Problem: Simplify x³·x⁴.
Recognize: The bases are the same and the powers are being multiplied.
Do it fast: Keep x and add the exponents: x³·x⁴=x³⁺⁴=x⁷.
Compare: x⁸÷x³=x⁸⁻³=x⁵. For (x²)⁴, multiply 2×4, giving x⁸.
Memory cue: product → add; quotient → subtract; power of a power → multiply.
Why it works
For x³·x⁴, the expanded product contains three x’s followed by four more x’s—a total of seven. The shortcut records that counting.
Five forms you should recognize
Keep the common base; add for multiplication and subtract for division.
Four groups of a³ contain twelve factors of a.
The outer power applies to every factor inside the parentheses.
The negative exponent creates a reciprocal; it does not make the value negative.
Work one operation at a time and rewrite the final answer with positive exponents.
Check before you commit
- Multiplying exponents in a product
- Adding exponents in a power of a power
- Making a negative exponent a negative number
- Forgetting coefficients
- Applying rules to different bases
- Treating a sum like a product
Do you need the lesson-or just practice?
One original question in each form recommends your next step. It does not yet verify mastery.
Work at the level you need.
Foundations
Build the core procedure with immediate explanations.
Core Practice
Use mixed forms with less scaffolding.
UPCAT-Style Transfer
Apply the competency in unfamiliar representations.
Ready to verify this competency?
A score of 5/5 verifies mastery. An unsuccessful attempt loads a different five-form bank.
Exponent Rules FAQ
Why are there two mastery sets?
A different five-question set appears after an unsuccessful attempt so memorizing one set does not verify mastery.
Does 5/5 mean I never need this topic again?
It verifies this competency today; revisit it later through mixed practice.
Continue your mathematics review.
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