Question
find missing exponent k5⋅k2kx = (k2)−2
Answers
Answered by
GPT 3.5
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.
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.
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