Laws of Exponents (Positive) - Solve + Match Worksheet

Apply the product rule of exponents (x^a * x^b = x^(a+b)) to simplify expressions.

Apply the power-of-a-power rule ((x^a)^b = x^(ab)) to simplify expressions.

Apply the quotient rule of exponents (x^a/x^b = x^(a-b)) to simplify expressions, including those with numeric coefficients.

Have students self-check as they go, since each of the 21 answer letters is used exactly once — a repeated or missing letter signals a simplification error before the worksheet is even turned in.

Use the answer key's expanded repeated-multiplication steps (e.g. showing x^2 * x^3 as x*x * x*x*x) as a model for students who need to see why the product rule works, not just memorise it.

Group problems by rule when reviewing: 1, 4, 7, 11, 17, 18, 19 use the product rule; 5, 8, 20 use power-of-a-power; 2, 6, 9, 12, 14, 15, 21 use the quotient rule; 3, 10, 13, 16 combine multiple steps.

Product rule of exponents — students simplify expressions like x^2 * x^3 and 4x^5 * 2x^3 across 7 of the 21 problems.

Power-of-a-power rule — students simplify expressions like (x^8)^2 and (3x^4)^2 across 3 problems.

Quotient rule of exponents — students simplify expressions like (x^5)^6/x^2 and 60x^12/3x^2 across 7 problems, several combining the quotient rule with the power rule.

Self-verification — students match each simplified answer to a unique letter, checking their own work against the one-to-one answer bank.