Question

Given the following expressions:

A) 53 * 5 - 4
B) 3⁵ / 3-⁶
C) 1 / (4³) * 1 / 4³
D) (-7)⁵ / (-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

Expressions A) and B) when simplified do not have values between 0 and 1, while expressions C) and D) do have values between 0 and 1 when simplified using operations of exponents.

Step-by-step explanation:

Part 1: Simplifying the given expressions using the operations of exponents:

• A) 53 * 5 - 4 = 265 - 4 = 261
• B) 3⁵ / 3⁻⁶ = 3⁵ * 3⁶ = 3¹¹ = 177147
• C) 1 / (4³) * 1 / 4³ = 1/64 * 1/64 = 1/4096
• D) (-7)⁵ / (-7)⁷ = 1/(-7)² = 1/49

Part 2: Determining whether each simplified expression's value is between 0 and 1:

• A) 261 is not between 0 and 1.
• B) 177147 is not between 0 and 1.
• C) 1/4096 is between 0 and 1.
• D) 1/49 is between 0 and 1.