Final answer:
The operations of exponents simplify the expressions A = 1/5, B = 19683, C = 1/1024, and D = 1/49 by adding or subtracting exponents for multiplication and division, respectively, with like bases.
Step-by-step explanation:
The expressions given require us to use the operations of exponents to simplify each one. The correct simplifications are as follows:
- A: 5³ • 5⁻⁴ uses the rule that when multiplying powers with the same base, you add the exponents. Thus, A = 5³+⁻⁴ = 5⁻¹ = 1/5.
- B: 3⁵/3⁻⁶ applies the rule that when dividing powers with the same base, you subtract the exponents. Hence, B = 3⁵-⁻⁶ = 3¹¹ = 19683.
- C: 1/4³ • 1/4² also involves multiplying powers with the same base, therefore you add the exponents. Since these are negative powers (being in the denominator), we add the exponents in a different way: C = 1/(4³ · 4²) = 1/4⁵ = 1/1024.
- D: -7⁵/-7⁷ is also a division of like bases, so we subtract the exponents. Here, the negatives cancel each other out, leaving us with D = 7⁵⁻⁷ = 7⁻² = 1/49.
Thus, the correct simplifications are:
- A = 1/5
- B = 19683
- C = 1/1024
- D = 1/49