Question

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

x = 6
x = 0
x = 9
x = 11
x = 1
x = 3

Answer 1

Answers
x = 6
x = 0
x = 9
x = 11
x = 1
x = 3

Answer 2

is this correct

Answer 3

To determine the missing exponent that would make the equation true, we need to simplify both sides of the equation.
The left side of the equation simplifies to k^(5+2-x) = k^(7-x).
The right side of the equation simplifies to (k^4)^(-2) = k^(-8).

To make the equation true, the exponents on both sides must be equal, so 7-x = -8.

By solving this equation, we can find the missing exponent:
7-x = -8
x = 7+8
x = 15.

Therefore, the missing exponent that would make the equation true is x = 15.

Answer 4

I apologize for the mistake in my previous response. Thank you for providing the options. Let's now check each option to determine which one makes the equation true.

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

1) If x = 6:
k^(5+2-6) = k^1
k^1 = k
This does not match the right side of the equation.

2) If x = 0:
k^(5+2-0) = k^7
k^7 = k^7
This matches the right side of the equation.

3) If x = 9:
k^(5+2-9) = k^-2
k^-2 ≠ k^-2
This does not match the right side of the equation.

4) If x = 11:
k^(5+2-11) = k^-4
k^-8 ≠ k^-4
This does not match the right side of the equation.

5) If x = 1:
k^(5+2-1) = k^6
k^6 ≠ k^-2
This does not match the right side of the equation.

6) If x = 3:
k^(5+2-3) = k^4
k^4 = k^4
This matches the right side of the equation.

Therefore, the missing exponent that would make the equation true is x = 0.

Answer 5

I apologize for the incorrect response in my previous answer. Let's reevaluate the equation to determine the correct missing exponent.

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

When we combine the exponents on the left side, we have k^(5 + 2 - x). On the right side, we have (k^2)^-2, which simplifies to k^(-4).

Therefore, we have k^(5 + 2 - x) = k^(-4).

To make the equation true, the exponents on both sides must be equal. Therefore, we have:

5 + 2 - x = -4

Simplifying this equation, we get:

7 - x = -4

To solve for x, we subtract 7 from both sides:

-x = -4 - 7
-x = -11

Finally, multiplying both sides by -1, we get:

x = 11

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