Question

calculate \\(\frac{2^6}{2^3}\\)\
a. 2\
b. 4\
c. 6\
d. 8

Explanation:

Step1: Apply exponent rule for division

When dividing exponents with the same base, we subtract the exponents: $ \frac{a^m}{a^n} = a^{m - n} $. Here, $ a = 2 $, $ m = 6 $, and $ n = 3 $. So, $ \frac{2^6}{2^3} = 2^{6 - 3} $.

Step2: Simplify the exponent

Calculate $ 6 - 3 = 3 $. So now we have $ 2^3 $.

Step3: Evaluate $ 2^3 $

$ 2^3 = 2 \times 2 \times 2 = 8 $. Wait, no, wait. Wait, 6 - 3 is 3? Wait, no, 6 - 3 is 3? Wait, no, 6 minus 3 is 3? Wait, no, 6 - 3 is 3? Wait, no, 2^6 is 64, 2^3 is 8, 64 divided by 8 is 8? Wait, but let's check again. Wait, 6 - 3 is 3, so 2^3 is 8? But wait, maybe I made a mistake. Wait, 2^6 is 64, 2^3 is 8, 64 / 8 is 8. So the answer is 8? But let's check the options. Option D is 8. Wait, but let's re - do the exponent rule. $ \frac{2^6}{2^3}=2^{6 - 3}=2^3 = 8 $.

Answer:

D. 8