Question

3^3 x (2^-16)^4/3^6

Answer 1

[AI-generated answer — Bot GPT 3.5]

To simplify the expression 3^3 x (2^-16)^4/3^6, we can start by evaluating the exponents.

First, let's simplify (2^-16)^4:

(2^-16)^4 = 2^(-16 * 4) = 2^-64

Next, let's simplify 3^3:

3^3 = 3^(3 * 1) = 3^3

Now that we have simplified the exponents, we can rewrite the expression as:

3^3 x 2^-64 / 3^6

Since the bases (3 and 2) are different, we cannot directly combine them. We will simplify each term separately:

3^3 = 3 * 3 * 3 = 27

2^-64 cannot be simplified further.

3^6 = 3 * 3 * 3 * 3 * 3 * 3 = 729

Now, we have:

27 x 2^-64 / 729

To simplify further, we can rewrite 2^-64 as (1/2)^64.

27 x (1/2)^64 / 729

Since 1/2 is the same as 2^-1, we can rewrite the expression as:

27 x (2^-1)^64 / 729

Using the property (a^m)^n = a^(m * n), we can simplify further:

27 x 2^(-1 * 64) / 729

27 x 2^-64 / 729

Now, we have:

27 / 729 x 2^-64

To simplify 27 / 729, we can notice that both numbers are divisible by 27:

27 / 729 = 1 / 27

So our expression becomes:

(1 / 27) x 2^-64

Now, we have simplified the original expression to (1 / 27) x 2^-64.