1. Fill in the blanks:
a. 3⁴ means three multiplied by itself four times.
3⁴ = 3 × 3 × 3 × 3 = 81
b. 2⁶ means two multiplied by itself six times.
2⁶ = 2 × 2 × 2 × 2 × 2 × 2 = 64
c. 8² means eight multiplied by itself two times.
8² = 8 × 8 = 64
d. 4⁴ means four multiplied by itself four times.
4⁴ = 4 × 4 × 4 × 4 = 256
e. 9³ means nine multiplied by itself three times.
9³ = 9 × 9 × 9 = 729
2. Identify the base and the exponent in the following exponential terms:
a. (−5/6)³: Base = −5/6 and Exponent = 3
b. (−5)³: Base = −5 and Exponent = 3
c. (13)⁻⁴: Base = 13 and Exponent = −4
d. (5.7)⁻⁶: Base = 5.7 and Exponent = −6
e. (6/7)⁴: Base = 6/7 and Exponent = 4
3. Write each of the following in the exponential form:
a. x × x × x × y × y = x³y²
b. 8 × 8 × 8 × 8 × 8 × 8 = 8⁶
c. (−14) × (−14) × (−14) × z × z = (−14)³z²
d. (−2/3) × (−2/3) × (−2/3) × (−2/3) = (−2/3)⁴
e. (−2) × (−2) × (−2) × (−2) × (−2) = (−2)⁵
4. Write each of the following in expanded form:
a. (−10)² = (−10) × (−10)
b. (12)³ = 12 × 12 × 12
c. (−7/9)⁴ = (−7/9) × (−7/9) × (−7/9) × (−7/9)
d. (0.7)³ = 0.7 × 0.7 × 0.7
e. (4/5)⁷ = (4/5) × (4/5) × (4/5) × (4/5) × (4/5) × (4/5) × (4/5)
f. (3.4)⁶ = 3.4 × 3.4 × 3.4 × 3.4 × 3.4 × 3.4
5. Complete the following table:
Exponential Form | Exponent/Power | Base | Expanded Form | Standard Form
5⁴ | 4 | 5 | 5×5×5×5 | 625
6³ | 3 | 6 | 6×6×6 | 216
(−3)² | 2 | −3 | (−3)×(−3) | 9
−3² | 2 | 3 | −(3×3) | −9
10² | 2 | 10 | 10×10 | 100
−4³ | 3 | 4 | −(4×4×4) | −64
(−4)³ | 3 | −4 | (−4)×(−4)×(−4) | −64
Parent Tip: Review the logic above to help your child master the concept of introduction to exponents worksheet.
