find missing exponent k5⋅k2kx = (k2)−2

Answer 1

To find the value of the missing exponent x, we can start by simplifying both sides of the equation.

On the left side, we can combine the k terms by adding their exponents. The exponent rule for multiplication of the same base is to add the exponents. Therefore, k^5 * k^2 = k^(5+2) = k^7.

On the right side, we can simplify the exponent by using the exponent rule for a negative exponent. The rule states that taking a number raised to a negative exponent is the same as taking the reciprocal of the number raised to the positive exponent. So, (k^2)^(-2) = 1 / (k^2)^2 = 1 / k^(2*2) = 1 / k^4.

Now, we have the simplified equation: k^7 = 1 / k^4.

To solve for x, we can compare the exponents on both sides of the equation. Since k^7 is equal to 1 / k^4, the exponents must be equal, so 7 = -4.

However, 7 is not equal to -4, so there is no value for x that satisfies the equation. Therefore, the missing exponent x does not exist.