Can you please let me know if I have worked this problem correctly:

425x11^y-7^z / 560x14^y-5^z-16

3y-2^ / 4x3^z-15^

I am not sure this is correct because we shouldn't have any negative exponents in our final answer.

Thank you

Your notation is not acceptable

did you mean y^11 instead of 11^y ?
is x a variable or a multiplication sign ?

The way you typed it we are dividing by only 560,
you will need brackets otherwise.

in your answer, -2^ and -15^ are meaningless.

this is how the question reads on my homework...I apologize for the confusion.

425X11^Y-7^Z
____________
560X14^Y-5^Z-16^

X to the 11th power....Y to -7th power
X to the 14th power....Y to -5th power
The answer is not supposed to have negatives in it. So, would i just divide 425/560 to get 3/4 and then subtract the exponents?

To check if you have worked the problem correctly, let's simplify the expression step-by-step.

The given expression is:
425x11^y-7^z / 560x14^y-5^z-16
3y-2^ / 4x3^z-15^

First, let's simplify the numerator of the fraction:
425x(11^y) - 7^z

The exponent rule states that for any number, say "a," raised to the power of "b" multiplied by "c" (a^(b*c)), it is equal to (a^b)^c. Using this rule, we can rewrite the expression as:
425x(11^y) - (7^z)

Next, let's simplify the denominator of the fraction:
560x(14^y) - 5^z - 16

Now, apply the exponent rule again to simplify the expression:
560x(14^y) - (5^z) - 16

Now, let's simplify further:
425x(11^y) - (7^z) / 560x(14^y) - (5^z) - 16

Finally, looking at the simplified expression, we can confirm that there are no negative exponents in the final answer.

Note: If you have additional terms or expressions, please provide them, and we can continue to simplify the whole expression.