Question

Вычислите 2^5×2^6/16^3

Answer 1

$2^{5} * 2^{6} / 16^{3} = 2^{5+6} / 2^{4*3}= 2^{11-12}= 2^{-1}= \frac{1}{2}$

Answer 2

To calculate the expression, you can use the rules of exponents:

1. When you multiply two numbers with the same base, you add their exponents.
2. When you divide two numbers with the same base, you subtract the exponent of the divisor from the exponent of the dividend.

Let's calculate step-by-step:

1. 2^5 × 2^6: Since the base is the same (2), we add the exponents: 5 + 6 = 11.

2. 16^3: 16 can be expressed as 2^4 (since 2^4 = 16). So, 16^3 = (2^4)^3 = 2^(4 × 3) = 2^12.

Now, the expression becomes:

(2^5 × 2^6) / 16^3 = 2^11 / 2^12

Now, when dividing with the same base, we subtract the exponents: 11 - 12 = -1.

So, the final answer is:

2^11 × 2^(-1) = 2^(11 - 1) = 2^10 = 1024.