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

k(5)⋅k(2)/k(x) = (k(2))(−2)

(1 point)
Responses

x = 11
x = 11

x = 0
x = 0

x = 3
x = 3

x = 9
x = 9

x = 6
x = 6

x = 1

1 answer

To solve the equation \( \frac{k(5) \cdot k(2)}{k(x)} = k(2)^{-2} \), we can first simplify the left-hand side.

Recall that \( k(a) \) represents a power of some base (like \( k(x) = k^x \)). Thus, we have:

  • \( k(5) = k^5 \)
  • \( k(2) = k^2 \)
  • \( k(x) = k^x \)

Now, substituting these into the equation, we get:

\[ \frac{k^5 \cdot k^2}{k^x} = k^2 \cdot k^{-2} \]

Next, simplify both sides:

Left side:

\[ \frac{k^5 \cdot k^2}{k^x} = \frac{k^{5+2}}{k^x} = \frac{k^7}{k^x} = k^{7-x} \]

Right side:

\[ k^2 \cdot k^{-2} = k^{2-2} = k^0 = 1 \]

Now we have:

\[ k^{7-x} = 1 \]

For this equation to hold true for any base \( k \) (where \( k \neq 0 \) or \( k \neq 1 \)), the exponent must be zero:

\[ 7 - x = 0 \]

Solving for \( x \):

\[ x = 7 \]

After analyzing the provided options, it looks like 7 is not listed. If you meant to include it, please check if there's an error. However, since it's not an option provided, if this is an error in the problem, I can't provide an answer based on the incorrect premise.

If you had \( x = 7 \) and if that was a choice, that would be the answer. Otherwise, if you stick with the choices you've given, none apply. Please double-check the equation or the options.

Similar Questions
  1. What is the missing exponent that would make this equation true?(k ^ 5 * k ^ 2)/(k ^ 2) = (k ^ 2) ^ - 2 (1 point) x = 11 x = 3 x
    1. answers icon 1 answer
  2. What is the missing exponent that would make this equation true?(k ^ 5 * k ^ 2)/(k ^ 2) = (k ^ 2) ^ - 2 (1 point) x = 11 x = 3 x
    1. answers icon 1 answer
    1. answers icon 1 answer
    1. answers icon 1 answer
more similar questions