What is the missing exponent that would make this equation true? k^-5 ⋅ k^2/k^x = (k^2)^−2

Answer 1

To find the missing exponent, we can simplify both sides of the equation.

On the left side, when we have the same base (k) with exponents, we can subtract the exponents:
k^-5 * k^2 = k^-3

Next, we can simplify the right side of the equation:
(k^2)^-2 = k^-4

Now, the equation becomes:
k^-3/k^x = k^-4

To divide with the same base, we can subtract the exponents:
-3 - x = -4

To solve for x, we can add 3 to both sides of the equation:
-3 - x + 3 = -4 + 3
- x = -1

Therefore, the missing exponent (x) that would make the equation true is -1.