Question

Given the following expressions:

A. 5³ • 5⁻⁴
B. 3⁵ over 3⁻⁶
C. 1/4³ • 1/4²
D. (-7)⁵ over (-7)⁷
Part 1: Use operations of exponents to simplify each expression (A-D). Include your work in your final answer.
Part 2: For each simplified expression (A-D), tell whether or not the expression has a value between 0 and 1.

Answer 1

In part 1, the expressions A, B, C, and D simplify to 1, 177,147, 1/64, and -1/2401 respectively. In part 2, only expression C has a value between 0 and 1.

Step-by-step explanation:

In part 1 of the question:

1. A. 5³ • 5⁻⁴ = (5 × 5 × 5) × (1/5 × 1/5 × 1/5) = 125 × 1/125 = 1
2. B. 3⁵ / 3⁻⁶ = (3 × 3 × 3 × 3 × 3) / (1/3 × 1/3 × 1/3 × 1/3 × 1/3 × 1/3) = 243 × 729 = 177,147
3. C. 1/4³ • 1/4² = 1/(4 × 4 × 4) × 1/(4 × 4) = 1/64
4. D. (-7)⁵ / (-7)⁷ = (-7) × (-7) × (-7) × (-7) × (-7) / (-7) × (-7) × (-7) × (-7) × (-7) × (-7) × (-7) = (-7) × (-7) × (-7) × (-7) × (-7) / (-7) × (-7) × (-7) × (-7) × (-7) × (-7) × (-7) = 1/(-7) × (-7) × (-7) = -1/2401

In part 2 of the question:

1. Expression A has a value of 1, which is not between 0 and 1.
2. Expression B has a value of 177,147, which is not between 0 and 1.
3. Expression C has a value of 1/64, which is between 0 and 1.
4. Expression D has a value of -1/2401, which is not between 0 and 1.