➕ Algebra 1 · Exponents and Polynomials
Laws of Exponents cheat sheet
Everything you need on one page. Print it, or switch on test-yourself mode to blur the answers and check your memory.
The four rules
- Product: am · an = am+n
- Quotient: am ÷ an = am−n (a ≠ 0)
- Power of a power: (am)n = amn
- Power of a product: (ab)n = an bn
Remember
- Product and quotient need the same base
- Level-down: × becomes +, ÷ becomes −, power of power becomes ×
- Coefficients are multiplied or divided like normal
Quick examples
- x5 · x2 = x7
- x9 ÷ x4 = x5
- (x3)4 = x12
- (2x)4 = 16x4
Traps
- x3 · x4 ≠ x12
- (2x)3 ≠ 2x3
- x3 + x4 cannot be combined
Formulas
- Product: am · an = am+n
- Quotient: am ÷ an = am−n (a ≠ 0)
- Power of a power: (am)n = amn
- Power of a product: (ab)n = an bn
Laws of Exponents cheat sheet from HighSchoolQ.com, for personal study use.