Exponent rules seem simple, but the SAT and ACT are designed to exploit the most common errors. Here are the 6 traps to avoid.
Mistake 1: Adding Exponents When Multiplying Bases
The trap: ?
Reality: You can only add exponents when the BASES are the same.
- ✓ (same base)
- ✓ (same exponent)
- = cannot be simplified ✗
Mistake 2: Distributing Exponents Over Addition
The trap: ?
Reality: . You MUST use FOIL or the binomial formula. The exponent only distributes over multiplication: .
Mistake 3: Negative Exponent Confusion
The trap: ?
Reality: . A negative exponent means reciprocal, NOT negative number.
Mistake 4: Zero Exponent on Negative Bases
The trap: ?
Reality: . ANY nonzero number to the power 0 equals 1. The only exception: is undefined.
Mistake 5: Power of a Power
The trap: ?
Reality: . Multiply the exponents, do not add them.
- (adding: same base, multiplication)
- (multiplying: power of a power)
Mistake 6: Fractional Exponents
The trap: ?
Reality: . The denominator is the root, the numerator is the power.
SAT & ACT Pro Tip
When you see exponents on the test, slow down for 5 seconds and identify which rule applies. The most common ACT/SAT strategy: convert everything to the same base, then compare exponents. For example, becomes , so , .
Practice exponent rules with our Exponent Rules lessons with interactive exercises.