Question

2^102 - 2^98/2^96

Answer 1

Please include the directions that came with this problem. could you possibly type this expression in Equation Editor for greater clarity?

Answer 2

\[2^{102} - 2^{98}\div2^{96}\] Evaluate the following expression

Answer 3

it also asks that I provide the answer in positive powers if required

Answer 4

That's SO much clearer! Thanks.
Are you dividing both terms on the left by 2^96, or only the 2nd term on the left?

Answer 5

I have been dividing just the second term. but the questions is written 2^102−2^98 over 2^96

Answer 6

In that case, you'd want to use parentheses to enclose the 2 terms on the left.

Answer 7

I am not sure if I am suppose to divide them both or not
I am really just trying to first simplify the exponents

Answer 8

First, I'll assume that we divide only the middle term by the last term:

2^102 - 2^98/2^96=

2^102 - 2^2

Answer 9

What is the factor common to these two terms?

Answer 10

Factor it out.

Answer 11

sorry by the two terms 2^102 and 2^2?

Answer 12

Yes (although I'm not sure I understand your question).

\[2^{102}-2^{2}=2^{100+2}-2^2=2^2(2^{100}-1)\]

Answer 13

Before we can come up with a definitive answer, we have to agree whether or not we're dividing both of the 2 terms on the left by 2^96, or just the middle term.

Answer 14

I think we are dividing both of them

Answer 15

\[(2^{102} - 2^{98}) \div 2^{96}\]

Answer 16

OK. Look at the first two terms first. Can the expression built from these two terms be factored?

OK...I'll go with your (very nice) expression.

You may either
(1) factor the quantity inside parentheses first, and then divide the result by 2^96, or
(2) Divide each term of the quantity inside parentheses by 2^96, separately.

Answer 17

so \[102 - 96 and 98 - 96?\]

Answer 18

\[2^{6} - 2^{2} ?\]