Exponents and Polynomials

Negative Exponents

A negative exponent means take the reciprocal: x^(-n) = 1/x^n. A coefficient stays in the numerator: c * x^(-n) = c/x^n. Negative exponents never appear in a simplified answer.

Example

Rewrite negative exponents as reciprocal factors with positive exponents.

highlighted = computed this step

Step 1 — Negative exponent

Set up the expression.

x−3x^{ -3 }

Step 2 — Rewrite reciprocal

Move x^-3 to the denominator as 1/x^3.

1x3\frac{ 1 }{x^{ \hl{3} }}

Step 3 — Coefficient example

Set up the expression.

4x−24 x^{ -2 }

Step 4 — Keep coefficient

Keep 4 on top and move x^-2 below as 4/x^2.

4x2\frac{ \hl{4} }{x^{ \hl{2} }}
negative-exponents Move the factor with the negative exponent to the denominator and make the exponent positive. The coefficient stays in the numerator unchanged.