➕ Algebra 1 · Exponents and Polynomials
Zero and Negative 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 two rules
- x0 = 1 (x ≠ 0)
- x−n = 1/xn (x ≠ 0)
- 1/x−n = xn (x ≠ 0)
- (a/b)−n = (b/a)n (a ≠ 0, b ≠ 0)
Why we choose them
- x3 ÷ x3 = 1, and the quotient rule would give x3−3 = x0
- x1 ÷ x4 = 1/x3, and the quotient rule would give x1−4 = x−3
Old rules still work
- Product: add exponents, x−6 · x2 = x−4
- Quotient: subtract exponents, x4 ÷ x10 = x−6
- Power of a power: multiply, (x5)−2 = x−10
- Finish with positive exponents
Traps
- 2−3 = 1/8, not −8
- 3x−2 = 3/x2, but (3x)−2 = 1/(9x2)
- −30 = −1, but (−3)0 = 1
- 00 is left undefined
Formulas
- Zero exponent: a0 = 1 (a ≠ 0)
- Negative exponent: a−n = 1/an (a ≠ 0)
- Moving back up: 1/a−n = an (a ≠ 0)
- Fraction base: (a/b)−n = (b/a)n (a ≠ 0, b ≠ 0)
Zero and Negative Exponents cheat sheet from HighSchoolQ.com, for personal study use.