Exponent Rules — Quick Reference Cheatsheet
A focused companion to the main Exponent Rules topic page on ACT Math.
ACT Math Pre-Algebra One-page reference
This is a one-page reference for Exponent Rules on the ACT math section. Apply x^a · x^b = x^{a+b}, (x^a)^b = x^{ab} and x^{−a} = 1/x^a. Use it as a printable cheatsheet before test day, or as a refresher right before you attempt the worked questions on the main Exponent Rules topic page.
What this topic is
A Exponent Rules question on the ACT tests basic arithmetic, fractions, percents, exponents, or simple statistics. These are the fastest-points questions on the test.
Core formulas you must memorise
- PEMDAS
- Percent ↔ decimal: divide or multiply by 100
- Mean / median / mode / range
- Probability = favourable / total
- Exponent rules: xᵃ · xᵇ = xᵃ⁺ᵇ
If any of these formulas are not yet automatic, drill them via the Pre-Algebra formula sheet. Memorisation is fastest when you write each formula out by hand five times in a row, then quiz yourself the next morning.
How to spot this question type on the test
ACT questions on Exponent Rules typically present in one of three ways: as a pure symbolic problem ("solve for x"), wrapped in a word problem (a real-world scenario you must translate), or hidden inside a longer multi-step question where Exponent Rules is just the first or last step. Train yourself to recognise the signature — a particular word, equation form, or diagram — and you will halve your reading time.
The 30-second decision
Slow on the read, fast on the math. Most pre-algebra mistakes are arithmetic slips made when rushing.
If you have 60 seconds before the question
Glance at the answer choices first. If they are widely spaced, estimate; if they are close, you must be exact. Sketch any diagram involved. Identify which of the formulas above applies. Then attempt — and if you cannot finish in 90 seconds, mark and move on. There is no penalty for guessing on either the SAT or the ACT, so always bubble in.
Drill set
Re-attempt the six worked Exponent Rules questions with this cheatsheet open. Then close it and re-attempt them from memory. If you can solve all six without peeking, this topic is locked in.
Related study material
For broader test-prep tactics, see our Exponent Rules strategy guide. For category-wide context, browse all Pre-Algebra topics. For score-targeted study plans, see the score-band guides.