Questions: Exponent Rules — Product, Power, and Quotient
3 questions to test your understanding
Score: 0 / 3
Question 1 Multiple Choice
Which expression is equivalent to x⁴ · x³?
Ax⁷
Bx¹²
Cx⁴³
D2x⁷
By the product rule, when multiplying like bases you add the exponents: x⁴ · x³ = x^(4+3) = x⁷. A common error is multiplying exponents (giving x¹²), which is what you do for the power rule (x⁴)³ — not for multiplication of separate factors.
Question 2 True / False
According to the power rule, (x³)⁴ = x⁷.
TTrue
FFalse
Answer: False
The power rule says (x^a)^b = x^(a·b), so (x³)⁴ = x^(3·4) = x¹². The answer x⁷ comes from incorrectly adding the exponents (3 + 4), which is what you do for the product rule, not the power rule. Mixing up these two operations is the most common error.
Question 3 Short Answer
A student claims that x³ · y² = xy⁵. What mistake did they make?
Think about your answer, then reveal below.
Model answer: They applied the product rule to different bases. The product rule (add exponents) only works when multiplying powers with the same base. Since x and y are different bases, x³ · y² cannot be simplified further.
The product rule requires identical bases: x^a · x^b = x^(a+b). Multiplying x³ · y² leaves bases x and y separate — you cannot combine their exponents. The expression is already in its simplest form.