Quotient of Powers Property Practice

Start with the three single rule sheets and keep the reference sheet nearby. Use the matching and true or false sheets to surface mistakes, then finish with a puzzle for review.

Divide powers with the same base, writing each quotient like 7⁸ ÷ 7⁵ as one power and a value. The quotient of powers rule says that to divide powers with the same base, you keep the base and subtract the bottom exponent from the top exponent. The directions on the page read: Write each quotient as one power on the first line. Then write its value on the second line as an integer or a fraction in simplest form. An answer key is included.

Yes, both. We made it for 8th grade exponents, and it works the same at home or at school. At home, a student can work through it alone and then go over it with you, which shows quickly what is solid and what needs another look. In class it works as independent practice, homework or a warm-up, and you can print one copy or a full set.

To multiply powers with the same base, keep the base and add the exponents. So 3⁴ × 3² = 3⁶. Product of Powers With Integer Bases also includes negative bases such as (−2)³ × (−2)⁴.

To raise a power to another power, keep the base and multiply the exponents, so (5²)³ = 5⁶. A common mistake is adding the exponents instead, which True or False, Exponent Property Statements asks students to catch.

Work the rule backward. In 5³ × 5 to the ? = 5⁹, the exponents must add to 9, so the missing exponent is 6. Two sheets practice this with numeric bases and with variable bases such as x and y.

Yes. The Properties of Exponents Reference Sheet lists each rule with its form, a plain explanation and a worked example. It is a handout, so it has no answer key.