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

Answer 1

To solve this equation, we can simplify both sides and equate the exponents:

On the left side of the equation:
k^5 ⋅ k^2/k^x = k^(5+2-x) = k^(7-x)

On the right side of the equation:
(k^2)^(-2) = k^(2*(-2)) = k^(-4)

Therefore, the equation can be rewritten as follows:

k^(7-x) = k^(-4)

To satisfy this equation, the exponents on both sides must be equal:

7 - x = -4

Adding x to both sides, we get:

7 = x - 4

Adding 4 to both sides, we get:

11 = x

Therefore, the missing exponent that would make the equation true is x = 11.