I can't quite write the problem, so I'll try to explain it as best I can. In exponents and in fractions...

(X/2) to the 3rd power times (X/2) to the 4th power...all over,or divided by, (X/2 to the 3rd power) to the 2nd power.
The book says the answer is X/2 to the 5th power. How is this answer found???? I keep getting X/2 to the 6th power ☹️

I answered above.. but this is clearer...

keep the base and add the powers when multiplying (x/2)^7

When raising a power to a power keep the base and multiply the 2 powers.

(x/2)^6

Again when dividing, keep the base and subtract the exponents. I still get (x/2)^1 or (x/2)

Sometimes books do have the wrong answer. I used to work for book companies and my job was to find the wrong answers so they could be fixed.

To solve this expression and determine why the answer is X/2 to the 5th power, let's break it down step by step:

First, let's simplify each of the exponents separately:

1. (X/2) to the 3rd power times (X/2) to the 4th power:
To multiply exponents with the same base, you add their exponents. In this case, we have (X/2) to the power of 3 multiplied by (X/2) to the power of 4.

(X/2) to the 3rd power multiplied by (X/2) to the 4th power can be written as (X/2)^(3+4).

So, (X/2) to the 3rd power multiplied by (X/2) to the 4th power simplifies to (X/2) to the 7th power.

2. (X/2) to the 3rd power to the 2nd power:
To raise a power to another power, you multiply their exponents. In this case, we have (X/2) to the power of 3 raised to the power of 2.

(X/2) to the 3rd power raised to the 2nd power can be written as (X/2)^(3*2).

So, (X/2) to the 3rd power to the 2nd power simplifies to (X/2) to the 6th power.

Now that we have simplified both parts of the expression, we can divide them:

(X/2) to the 7th power divided by (X/2) to the 6th power = (X/2)^(7-6) = (X/2)^1.

And any expression raised to the power of 1 remains unchanged.

Therefore, the final answer is (X/2)^1, which is equal to X/2.

The book's answer of X/2 raised to the 5th power may be incorrect, as it seems to be inconsistent with the calculations. Double-checking the book's answer or referring to the original problem's statement might be necessary.