Question

Given the following expressions:

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

Answer 1

In expression A, 53 • 5–4 simplifies to 1/5. In expression B, 3⁵/3⁻6 simplifies to 177147. In expression C, (1/4)³ • (1/4)² simplifies to 1/1024. In expression D, (-7)⁵/(-7)⁷ simplifies to 1/49.

Step-by-step explanation:

A. 53 • 5–4:

In this expression, we have a base of 5 and two exponents, 3 and -4. To simplify, we multiply the base and add the exponents:

53 • 5–4 = 5(3 + -4) = 5⁻¹ = 1/5

B. 3⁵/3⁻6:

Here, we have the same base of 3 and exponents of 5 and -6. To simplify, divide the bases and subtract the exponents:

3⁵/3⁻6 = 3^(5 - -6) = 3¹¹ = 177147

C. (1/4)³ • (1/4)²:

In this expression, we have a base of 1/4 and exponents of 3 and 2. To simplify, multiply the base and add the exponents:

(1/4)³ • (1/4)² = (1/4)^(3 + 2) = (1/4)⁵ = 1/1024

D. (-7)⁵/(-7)⁷:

Here, we have a base of -7 and exponents of 5 and 7. To simplify, divide the bases and subtract the exponents:

(-7)⁵/(-7)⁷ = (-7)^(5 - 7) = (-7)⁻² = 1/49