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Exponent rules practice
Exponent rules describe repeated multiplication. Check the operation first: multiplying powers, raising a power, and adding terms require different reasoning.
By ExamCat · Original study lesson · Published September 24, 2026
Understand the method
For the same nonzero base, multiply powers by adding exponents and divide by subtracting exponents. Raising a power to another power multiplies exponents. A negative exponent means reciprocal, not a negative value.
Worked example, step by step
Simplify (x³ × x⁴)/x² for x ≠ 0.
- Combine the numerator: x³ × x⁴ = x⁷.
- Divide by x²: x⁷/x² = x⁵.
- Record x ≠ 0 from the original denominator.
- Check with x = 2: (8 × 16)/4 = 32, equal to 2⁵.
A mistake to watch for
You cannot apply the multiplication rule to x³ + x⁴. The plus sign joins different terms rather than multiplying factors. Also, simplification does not remove restrictions inherited from the original expression.
Try it yourself: three questions
Write an answer before opening the explanation. For calculations, keep your units and intermediate steps; for concepts, state the reason for your choice.
1. Simplify (a²)³.
Show answer and explanation
a⁶, because three groups of a² contain six factors of a.
2. Evaluate 2⁻³.
Show answer and explanation
1/2³ = 1/8. It is positive, not −8.
3. Simplify y⁵/y⁵ for y ≠ 0.
Show answer and explanation
1. This agrees with y⁰ = 1 for a nonzero base; the original expression is undefined at y = 0.
Build your next practice session
Mark the first step where your reasoning differed from the explanation. Turn that step into a question, answer it without looking, then change one condition in the example and explain what would change. A correct guess is a reason to revisit the method.
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