Question

Find the missing factor. Write your answer in exponential form.

"2 to the power of 4 equals 2 to the power of negative 7 times what?"

Answer 1

The missing factor in the equation is 2 to the power of 11. This is found by equating the exponents since the bases are the same and solving for the unknown exponent.

Step-by-step explanation:

To find the missing factor, we will use the properties of exponents. Since we know that 2 to the power of 4 equals 2 to the power of negative 7 times some number, we can represent the missing number as 2x. We want to find x such that 24 = 2-7 × 2x. To find x, we can equate the exponents on both sides since the bases are the same:

4 = -7 + x

Now, we can solve for x by adding 7 to both sides:

4 + 7 = x

11 = x

Therefore, the missing factor is 2 to the power of 11 or in exponential form 211.