ACT Math: Exponent Rules and When to Break Them

Master these five rules and you solve 80% of ACT exponent problems: (1) x^a*x^b=x^(a+b) (multiply: add exponents), (2) x^a/x^b=x^(a-b) (divide: subtract exponents), (3) (x^a)^b=x^(ab) (power of a power: multiply exponents), (4) x^0=1 (anything to the zero power is 1), (5) x^(-a)=1/x^a (negative exponent flips to fraction). Write these on an index card. These five rules cover 99% of ACT exponent questions.

Example chain: Simplify (3^2*3^4)/(3^3). Step 1: numerator = 3^(2+4)=3^6. Step 2: divide = 3^(6-3)=3^3=27. Most students make mistakes here because they forget which rule applies when. Pre-drill until the rules are automatic.

Mistake 1: (x^2)^3≠x^5. It equals x^6 (multiply exponents, not add them). Mistake 2: x^2+x^3≠x^5. Exponent rules only apply to multiplication and division, not addition. You cannot simplify x^2+x^3. Mistake 3: (2x)^2≠2x^2. It equals 4x^2 (the 2 is also squared). Write these three mistakes on flashcards and drill them until you automatically catch them.

If you make any of these mistakes regularly, spend 10 minutes today drilling each one. Solve five versions of each mistake, correcting yourself each time. This muscle-memory training cuts errors on test day by half.

Solve these in order: (1) 2^3*2^2, (2) (5^2)^3, (3) 10^0, (4) 3^(-2), (5) x^5/x^2, (6) (2x)^3, (7) 2^3+2^2 (trick: don't simplify), (8) x^4*x^(-2). Write your work for each one and check against the answer key. If you miss any, redo that specific rule five more times.

Answers: (1) 2^5=32, (2) 5^6, (3) 1, (4) 1/9, (5) x^3, (6) 8x^3, (7) 8+4=12 (no simplification), (8) x^2. If you missed problem 7, you're not alone—the trick is recognizing when the rule doesn't apply.

Exponent problems appear throughout ACT Math: in algebra, sequences, exponential growth, and advanced functions. Master these five rules and you unlock points across multiple question types. Most students lose 1-2 points per test on careless exponent errors that a quick review session eliminates entirely.

Spend one week drilling these rules. By test day, you will solve exponent problems instantly and correctly, freeing mental energy for harder problems. That's an easy 1-2 point gain.