Zero and Negative Exponents With Fraction Bases

Use these pages after students are confident with positive exponents. Point students to the explainer at the top of each sheet before they start.

Simplify 20 powers like 2.5 to the negative 2 and 2/5 to the negative 2 by flipping the base. A negative exponent flips the base: (3 5) −2 = (5 3) 2 = 25 9 = 2 7 9, and any nonzero base to the 0 power is 1. The directions on the page read: Simplify. Use decimals for decimal bases and mixed numbers for improper fractions. An answer key is included.

Yes, both. We made it for 6th Grade exponents, and the page works the same whether it lands on a kitchen table or a center rotation. At home, most families go through it together and talk the answers out loud, and that talking is where most of the learning happens with negative numbers and exponents. In class it runs well as independent work while you pull a small group. Print one copy or thirty, whichever the day needs.

Any nonzero number to the 0 power is 1, so 3 to the 0 power = 1 and 3/7 to the 0 power = 1.

Flip the fraction and make the exponent positive. 3/5 to the negative 2 = 5/3 squared = 25/9 = 2 7/9.

Three negative factors multiply to a negative number, so (−2) × (−2) × (−2) = −8. With an even exponent, like (−10) squared = 100, the value is positive.