What is the missing exponent that would make this equation true?

Question

(k^5 time k^2)/(k^x) = (k^2)^-2

Answer 1

The missing exponent is 7.

Given equation: (k^5 * k^2)/(k^x) = (k^2)^-2

Using the property of exponents that states (a^m * a^n) = a^(m+n):

(k^(5+2))/(k^x) = k^-4

Simplifying further:

k^7/k^x = k^-4

Using the property of exponents that states a^m/a^n = a^(m-n):

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

Using the property of exponents that states (a^m)^n = a^(m*n):

k^(7-x) = k^(-4*1)

Therefore, 7-x = -4

Solving for x:

7 - x = -4

x = 7 + 4

x = 11

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