Question

an equation is shown, where x and y represent integers.
5^x/ 5^y = 5^-3

Answer 1

what are the possible values of x and y?
x=__________
y= ___________

Answer 2

To solve this equation, we can use the property of exponents that states:

a^(m/n) = (a^m)^(1/n)

Using this property, we can rewrite the equation as:

(5^x)/(5^y) = 5^(-3/1)

Simplifying further, we have:

5^(x - y) = 5^(-3)

Since the bases on both sides of the equation are the same, we can equate the exponents:

x - y = -3

This is the simplified equation representing the relationship between x and y.

Answer 3

To determine the possible values of x and y, we need additional information or constraints for the equation. With the given equation 5^(x-y) = 5^(-3), we can't determine the specific values of x and y without more context.

However, if we assume that x and y are integers, we can solve for the possible values by equating the exponents:

x - y = -3

In this case, there are infinitely many potential solutions for x and y. For example:

x = -3, y = 0
x = -2, y = 1
x = -1, y = 2
x = 0, y = 3

These are just a few examples, but there are infinitely many integer solutions.