6 over x to the 10th times x to the 17th over 15
It's easier to visualize if you write it as
(6/x^10)*(x^17)/15
which clearly becomes
= (2/5)*x^7
To simplify this expression, we can combine the terms in the numerator (6 over x to the 10th) and the terms in the denominator (x to the 17th over 15).
To combine fractions, we need a common denominator. In this case, the common denominator is x to the 10th times 15, which is the least common multiple of x to the 10th and 15.
First, let's find the least common multiple (LCM) of x to the 10th and 15.
The prime factorization of 15 is 3 * 5, and x to the 10th is already in its simplest form.
To find the LCM, we need to take the highest power of each prime factor that appears in either expression.
For x to the 10th and 15, the LCM is x to the 10th times 3 times 5, which simplifies to 3x^10 * 5.
Now we can rewrite the expression with the common denominator:
(6 * 5) / (x^10 * 3)
Simplifying further, we get:
30 / (3 * x^10)
Then, we can simplify the denominator:
30 / (3 * x^10) = 10 / (x^10)
So the simplified expression is 10 / (x^10).