The Laws of Exponents

Mathematics · Algebra · ages 12-14

Name ______________________ Date ____________

Simplify 2^8 / 2^3. Write your answer as a power of 2.
- 2^5
- 2^11
- 4^5
- 2^24
Simplify 5^3 x 5^4. Write your answer as a power of 5.
- 5^7
- 5^12
- 25^7
- 25^12
What is 2³ × 2⁴ written as a single power of 2?
- 2⁷
- 2¹²
- 4⁷
Any nonzero number raised to the power 0 equals 1.
Circle one: True False
Malik simplifies 4² × 4³ and writes 16⁵. What is the correct answer?
- 4⁶
- 4⁵
- 16⁵
Simplify 10^4 x 10^-2. Give your answer as an ordinary number.
Answer: ______________
Evaluate 2^-3. Give your answer as a fraction.
- 1/8
- -8
- -6
- 8
2⁻³ = 1/n. What is n?
Answer: ______________
Which statement is correct?
- 3² × 3³ = 3⁵
- 3² × 3³ = 9⁵
- 3² × 3³ = 3⁶
2⁴ × 2⁻⁶ = 1/n. What is n?
Answer: ______________

Answer key

For grown-ups. Fold this page away before handing over the rest.

2^5 · Keep the base 2 and subtract: 8 - 3 = 5.
5^7 · Keep the base 5 and add the powers: 3 + 4 = 7.
2⁷ · Add the exponents because the bases match: 3 + 4 = 7, so 2³ × 2⁴ = 2⁷.
True · This matches the pattern from dividing: 7³ ÷ 7³ = 7⁰, and a number divided by itself is always 1.
4⁵ · The base stays 4; only the exponents add: 2 + 3 = 5, so 4² × 4³ = 4⁵, not 16⁵.
100 · 10^4 x 10^-2 = 10^2 = 100.
1/8 · A negative power flips to a fraction: 2^-3 = 1/2^3 = 1/8.
8 · A negative exponent flips to a fraction: 2⁻³ = 1/2³ = 1/8, so n = 8.
3² × 3³ = 3⁵ · Keep the base the same and add the exponents: 2 + 3 = 5, so 3² × 3³ = 3⁵.
4 · Add the exponents: 4 + (−6) = −2, so 2⁴ × 2⁻⁶ = 2⁻² = 1/4, which means n = 4.