ACT-Style: Exponent Rules

ACT Math · Axiom Academy

EXAMPLE ACT-Style: Exponent Rules Simplifying a power-of-a-power expression the way it actually shows up on the test Simplify the expression so that it has a single term with a positive exponent. Every layer of this expression asks for a different exponent rule — mixing them up is exactly how the wrong answer choices get built. Power to a power: (a^m)^n = a^ mn — the exponents MULTIPLY, they never add. , not x^ 3+2 =x^5 . Distribute over a product: (ab)^n = a^n b^n — the coefficient gets raised to the power too. (2x^3)^2 = 2^2 (x^3)^2 = 4x^6 , not 2x^6 . Product rule: — the exponents ADD (with their signs), they never multiply. . On the ACT, exponent problems are rarely wrong because of arithmetic — they're wrong because a power-to-a-power step got treated like a product-rule step, or vice versa. Naming which rule applies at each stage is the real skill.

This is the written version of the interactive lesson above. See the full ACT Math course.