Evaluate Powers With Negative 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.

Evaluate 12 expressions with negative bases in parentheses, such as (−8) cubed + (−9) cubed. A negative base with an odd exponent gives a negative value: (−2) 3 = (−2) × (−2) × (−2) = −8. With an even exponent the value is positive. The directions on the page read: Find the value of each expression. Use the space under each one for your work. 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.