Algebra Foundation Quiz #2 Question 7

Not sure what I’m doing wrong here. That was my approach:

double the reciprocal of a number 8 times

The doubling occurs 8 times

I’m afraid I still don’t get it…

double the reciprocal once is 1/x x 2

double the reciprocal twice is 1/x x 2 + 1/x x 2

and so on…

My interpretation:

Doubling the reciprocal one time means \frac{1}{x} \times 2.
Doubling the reciprocal two times means \frac{1}{x} \times 2 \times 2, or \frac{1}{x} \times 2^2.
Doubling the reciprocal three times means \frac{1}{x} \times 2 \times 2 \times 2, or \frac{1}{x} \times 2^3.
Doubling the reciprocal four times means \frac{1}{x} \times 2 \times 2 \times 2 \times 2, or \frac{1}{x} \times 2^4.
And so forth.

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