Negative Exponents Practice Test

About This Negative Exponents Practice Test

This test emphasizes the central rule a⁻ⁿ = 1/aⁿ. Students apply that rule to numbers, variables, fractions, products, quotients, powers of powers, and scientific notation.

The questions also distinguish (−3)⁻² from −3⁻², test equations containing reciprocal powers, and reinforce that a negative exponent does not make a value negative.

Skills Covered

Rewriting with positive exponents, adding and subtracting signed exponents, applying powers to products and quotients, simplifying multivariable expressions, solving reciprocal equations, and identifying restrictions.

Key Rules

1. A negative exponent creates a reciprocal.
2. When multiplying like bases, add signed exponents.
3. When dividing like bases, subtract denominator exponents.
4. A factor moved across a fraction bar changes the sign of its exponent.

Common Mistakes to Avoid

Do not confuse a negative exponent with a negative coefficient, forget to apply an outside power to every factor, or cancel a zero-denominator restriction.

Practice Format

Every solution shows the exponent rule used and explains the specific arithmetic or structural error behind each distractor.