Zero and Negative Exponents

Algebra 1 · Axiom Academy

LESSON Zero and Negative Exponents Discover why any nonzero number to the zero power equals 1, and why a negative exponent means a reciprocal — by following one pattern. Start with powers of 2 you already trust. Reading down the list, the exponent drops by 1 and the value is cut in half each time — every step is a . Going down one row divides the value by 2 The pattern points to 2^0 = 1 . Here is a second, independent reason it must be true — divide a power by itself two different ways and compare. Divide 2^3 by itself. The quotient rule subtracts the exponents: But a nonzero number over itself is just 1 : The same quantity can't be two different things, so 2^0 and 1 are the same number. Why stop at zero? Keep dividing by 2. The exponents keep dropping — into the negatives — and the values keep halving, so they become fractions. A negative exponent says: move the base across the fraction bar and flip the sign of the exponent to positive. The animation does exactly that move. Put both rules to work. Watch the headline problem get solved step by step, then check the others. Example 1 — a negative power of a number Apply the reciprocal rule, then evaluate the power: Example 2 — only one factor is affected The exponent sits on x alone, so only x moves down; the 3 stays put: Example 3 — a negative power of a fraction Flip the fraction, then square the result:

This is the written version of the interactive lesson above. See the full Algebra 1 course.