College Algebra / Unit 1 Alg 037 worked example, 60 to 90 seconds
Simplifying with the Exponent Rules
The idea
Simplifying with the exponent rules means applying the product, quotient, power, zero, negative, and power-of-a-product rules until each base appears once, with a positive exponent.
In practice
Simplify (2a³b²)² · a⁻⁴. The power of a product rule squares each factor: 2²a⁶b⁴ = 4a⁶b⁴. The product rule absorbs a⁻⁴: a⁶ · a⁻⁴ = a². The result is 4a²b⁴ — each base once, every exponent positive. The order of moves is flexible; the finish line is fixed: no repeated bases, no negative exponents, no zero exponents left unevaluated. A second run: simplify x⁵ · x⁰ / x³. The zero exponent rule collapses x⁰ to 1, and the quotient rule finishes: x⁵ / x³ = x². Two rules, two moves, done — and every path through the rules lands on the same simplified form.
Where people slip
Apply the outer exponent to every factor inside the parentheses, the coefficient included.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
Builds on
- Nothing. This is a starting point.
Unlocks
- Nothing yet depends on this.
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