I was wondering if you can describe the steps in getting the solution to the problem below. I have the solution of 5/3 in the back of a book, but I have no idea how that answer was reached.

2raised to the 100th power + 2raised to the 98th power divided by 2raised to the 100th power - 2raised to the 98th power

Hi,

2 raised to the 100th power is

2 2 2 ... 2 2 2

where the 2 is multiplied by itself 100 times. This can be written

(2 2 2 ... 2) 2 2

where the 2 is multiplied by itself 98 times then twice more. That is

2¹⁰⁰ = 2⁹⁸ 2²

Thus the numerator is

2¹⁰⁰ + 2⁹⁸
= 2⁹⁸ 2² + 2⁹⁸
= 2⁹⁸ (2² + 1)
= 2⁹⁸ 5

Write the term 2¹⁰⁰ in the denominator the same way and see if that helps.

Penny

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