k^5 x k^2/k^x = (k^2)^-2
What is the missing exponent that would make this expression true
To solve this, we need to use the properties of exponents.
First, rewrite both sides of the equation with the same base, which is k, since the bases must be equal for the exponents to be equal.
k^5 x k^2/k^x = (k^2)^-2
Now, apply the rule of multiplying exponents with the same base.
k^(5+2)/k^x = k^(-4)
Combine the exponents on the left side.
k^7/k^x = k^(-4)
Now, apply the rule of dividing exponents with the same base. Subtract the exponent of the denominator from the exponent of the numerator.
k^(7-x) = k^(-4)
For the two sides of the equation to be equal, the exponents must be equal.
7 - x = -4
Solve for x.
7 = x - 4
Add 4 to both sides.
7 + 4 = x
x = 11
Therefore, the missing exponent that would make the expression true is x = 11.