OG Negative Exponents Q

AbeNeedsAnswers wrote:The value of [2^(−14) + 2^(−15) + 2^(−16) + 2^(−17)]/ 5 is how many times the value of 2^(−17)?

A. 3/2
B. 5/2
C. 3
D. 4
E. 5

C

Say the value of [2^(−14) + 2^(−15) + 2^(−16) + 2^(−17)]/ 5 is x times the value of 2^(−17).

We then need to get the value of x.

=> [2^(−14) + 2^(−15) + 2^(−16) + 2^(−17)] / 5 = 2^(−17)*x

Taking 2^(−17) common from the RHS. We get,

2^(−17)[[2^(3) + 2^(2) + 2^(1) + 1] / 5] = 2^(−17)*x

=> [2^(3) + 2^(2) + 2^(1) + 1] / 5 = x; 2^(−17) gets cancelled

= [8 + 4 + 2 + 1] /5 = x

= [15] /5 = x

[spoiler]x = 3[/spoiler].

The correct answer: C

Hope this helps!

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AbeNeedsAnswers wrote:The value of [2^(−14) + 2^(−15) + 2^(−16) + 2^(−17)]/ 5 is how many times the value of 2^(−17)?

A. 3/2
B. 5/2
C. 3
D. 4
E. 5

C

Here's my solution

AbeNeedsAnswers wrote: ↑

Wed Jul 19, 2017 10:04 pm

The value of [2^(−14) + 2^(−15) + 2^(−16) + 2^(−17)]/ 5 is how many times the value of 2^(−17)?

A. 3/2
B. 5/2
C. 3
D. 4
E. 5

C

We can create the following equation in which k is an integer:

[2^(-14) + 2^(-15) + 2^(-16) + 2^(-17)] / 5 = (k)(2^-17)

[2^(-14) + 2^(-15) + 2^(-16) + 2^(-17)] = (k)(2^-17)(5)

Let’s multiply each side of the equation by 2^17:

2^17[2^(-14) + 2^(-15) + 2^(-16) + 2^(-17)] = (2^17)(2^-17)(k)(5)

2^3 + 2^2 + 2^1 + 1 = 5k

(8 + 4 + 2 + 1) = 5k

15 = 5k

3 = k

Answer: C