How do you simplify this equation:

(x^a+b)^a-b / (x^a-2b) ^ a+2b

without grouping symbols, it is anyones guess what the fraction is.

Sorry!

(x^ a+b) ^ (a-b) / (x^a-2b) ^ (a+2b)

simplify the expression using the properties of rational exponents 13 to ...

To simplify the given equation, let's break it down step by step.

Step 1: Simplify the numerator.
In the numerator, (x^a+b)^a-b, we can apply the exponent rules. According to the rule (a^b)^c = a^(b*c), we can simplify the expression as follows:
(x^a+b)^a-b = x^((a+b)*(a-b))

Step 2: Simplify the denominator.
In the denominator, (x^a-2b)^a+2b, again, we can apply the exponent rules. Using the same rule mentioned above, we simplify:
(x^a-2b)^a+2b = x^((a-2b)*(a+2b))

Step 3: Combine the numerator and denominator.
Now that we have simplified both the numerator and the denominator, the simplified equation becomes:
x^((a+b)*(a-b))/x^((a-2b)*(a+2b))

Step 4: Apply the quotient rule of exponents.
Using the quotient rule of exponents, when dividing two exponential expressions with the same base, we subtract the exponents. Therefore, in our equation, subtracting the exponents gives us:
x^(((a+b)*(a-b))-((a-2b)*(a+2b)))

Step 5: Simplify the exponent expression.
Now, it's time to simplify the exponent expression. Distribute and simplify:
(a+b)*(a-b) = a^2 - b^2
(a-2b)*(a+2b) = a^2 - (2b)^2 = a^2 - 4b^2

Substituting these values back into our equation:
x^(((a+b)*(a-b))-((a-2b)*(a+2b))) = x^(a^2 - b^2 - (a^2 - 4b^2))

Step 6: Simplify further.
Now, we need to simplify the expression inside the exponent:
a^2 - b^2 - (a^2 - 4b^2) = -3b^2

Replacing this value in our equation, we get:
x^(-3b^2)

So, the simplified equation is x^(-3b^2).