(-3)² means (-3) × (-3) = 9. The parentheses make the exponent apply to the negative sign as well, and a negative times a negative is positive. This is different from -3² = -(3 × 3) = -9, where the exponent applies only to 3.
Question 2 True / False
The expression 2⁵ equals 10.
TTrue
FFalse
Answer: False
2⁵ means 2 × 2 × 2 × 2 × 2 = 32, not 2 × 5 = 10. Exponents represent repeated multiplication, not multiplication. Confusing 2⁵ with 2 × 5 is the single most common exponent error — the exponent counts how many times the base appears as a factor.
Question 3 Short Answer
Using the definition of exponents as repeated multiplication, explain why 2³ × 2⁴ = 2⁷.
Think about your answer, then reveal below.
Model answer: 2³ × 2⁴ = (2 × 2 × 2) × (2 × 2 × 2 × 2) = 2⁷, because you are combining 3 twos and 4 twos into a single product of 7 twos.
Writing out each factor explicitly shows that multiplication joins two groups of repeated factors into one. The exponents add because you are counting the total number of times the base appears: 3 + 4 = 7. This is the intuition behind the product-of-powers rule you will learn next.