Question

What is the missing exponent that would make this equation true? k^-5 • k^2/k^x = (k^0) ^-2

Answer 1

To determine the missing exponent, we can simplify the equation.

First, on the left side of the equation, we can apply the properties of exponents to combine the k^-5 term with the k^2 term by adding their exponents:

k^-5 • k^2 = k^(-5+2) = k^-3

Next, we divide k^-3 by k^x. When dividing, we subtract the exponents:

k^-3 / k^x = k^(-3-x)

On the right side of the equation, we have (k^0)^-2, which implies that anything raised to the power of 0 is equal to 1. Therefore, (k^0) ^-2 = 1^-2 = 1.

Now we have the equation k^(-3-x) = 1.

For the equation to be true, the power of k on both sides must be equal. Therefore, the missing exponent x would be:

-3 - x = 0

To solve for x, we can add 3 to both sides of the equation:

-3 - x + 3 = 0 + 3
- x = 3

Now, we can multiply both sides by -1 to isolate x:

x = -3

Therefore, the missing exponent x that would make the equation true is -3.