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 ☹️
it's a lot easier without all those words:
(x/2)^3 * (x/2)^4
----------------------
((x/2)^3)^2
= (x/2)^7 / (x/2)^6
= x/2
Hmmm. Not what you want. I suspect a typo somewhere.
Since they are all the same, let x represent x/2. Online "^" is used to indicate an exponent, e.g., x^2 = x squared
(x^3 * x^4)/(x^3)^2
When multiplying/dividing, exponents are added/subtracted respectively.
(x^3 * x^4) = x^7
(x^3)^2 = x^6
Do you have typos?
Let me try writing it again...
(X/2)^3*(X/2)^4
---------------------
(X/2^3)^2
How do you get X/2^5????
I don't. I still get:
(x/2)^7/(x/2)^6 = x/2
If you do not have a typo, there might be a typo in the text answers. Ask your teacher.
To find the answer, let's break down the problem step by step.
We want to simplify the expression:
[(X/2)^3 * (X/2)^4] / [(X/2)^3]^2
First, let's simplify the numerator by multiplying the two exponents:
(X/2)^3 * (X/2)^4 = (X/2)^(3+4) = (X/2)^7
Now, let's simplify the denominator by squaring the exponent:
(X/2)^3^2 = (X/2)^(3*2) = (X/2)^6
So we have:
(X/2)^7 / (X/2)^6
To divide two numbers with the same base, we subtract the exponents:
(X/2)^7 / (X/2)^6 = (X/2)^(7-6) = (X/2)^1
And any number raised to the power of 1 remains unchanged, so we have:
(X/2)^1 = X/2
Therefore, the final answer is X/2. The book is correct.
If you were getting X/2^6 as your answer, it seems that you might have made a mistake when multiplying the exponents in the numerator. Make sure to review the exponent rules and double-check your calculations.