We can simplify the left side of the equation first:
(k^5)(k^2) / (k^x) = k^(5+2) / k^x = k^7 / k^x
Using the rule of exponents that states a^m / a^n = a^(m-n), we have:
k^7 / k^x = k^(7-x)
Now we can rewrite the equation as:
k^(7-x) = (k^2)^-2 = k^(-4)
For the equation to be true, the exponents on both sides of the equation must be equal. This means:
7 - x = -4
Solving for x, we find:
x = 7 + 4 = 11
Therefore, the missing exponent that would make the equation true is x = 11. The correct answer is D: x = 11.
What is the missing exponent that would make this equation true?
(k^5 time k^2)/(k^x) = (k^2)^-2
A: x = 1
B: x = 6
C: x = 9
D: x = 11
E: x = 3
F: x = 0
1 answer