Question

ahhh, negative exponent: 2^-4 + 2^-6 / (2^-3) = ?

Answer 1

2^-4 + 2^-6 / (2^-3) = 1/2^4 + 1/2^6 / 1/2^3
= 2^2+1 / 2^6 / 1/2^3

Answer 2

= 2^2 + 1/2^6 x 2^3 / 1
= 2^2+1/2^3
= 5/8

Answer 3

Why is the second step: 2^2+1 / 2^6 / (1/2^3)? omg I'm still so confused

Answer 4

i thought I got it but ahh.

Answer 5

\[\frac{2^{-4} + 2^{-6} }{ 2^{-3}}?\]

Answer 6

If the answer is 5/8, then it's \[\frac{2^{-4} + 2^{-6} }{ 2^{-3}}\]

\[\frac{2^{-4} + 2^{-6} }{ 2^{-3}}\]\[\large = \frac{\frac{1}{2^{4}} + \frac{1}{2^{6}} }{ \frac{1}{2^{3}}}\]\[\large = \frac{\frac{2^2}{2^{4+2}} + \frac{1}{2^{6}} }{ \frac{1}{2^{3}}}\]\[\large = \frac{\frac{2^2+1}{2^{6}} }{ \frac{1}{2^{3}}}\]\[\large = \frac{\frac{5}{2^{6}} }{ \frac{1}{2^{3}}}\]\[ = 2^3(\frac{5}{2^{6}}) \]\[= \frac{5}{2^{6-3}} \]\[= \frac{5}{2^{3}} \]\[= \frac{5}{8} \]

Answer 7

why is it 2^2 for second step? :$

Answer 8

Multiply both denominator and numerator by 2^2 so that you can get 2^6 for the denominator and do the addition for the fractions

Answer 9

wait so first it's 1/2^4 + 1/2^6 and so why is it now 2^2? I subtract exponent 6 from exponent 4?

Answer 10

\[\frac{1}{2^4} + \frac{1}{2^6} = \frac{1\times 2^2}{2^4 \times 2^2} + \frac{1}{2^6} = \frac{1\times 2^2}{2^{4+2}} + \frac{1}{2^6} = \frac{2^2}{2^{6}} + \frac{1}{2^6}\]Got it?

Answer 11

i'm so sorry but why 1 x 2^2?

Answer 12

Because you've multiply the denominator by 2^2, you can't change the value of the fraction. So, you need to do the same for numerator

Answer 13

ohh so for the denominator you multiplied 2^4 x 2^2 to get 2^6?

Answer 14

Yes.

Answer 15

thank you!

Answer 16

Are you sure you understand this time?

Answer 17

yes, now I'm sure. Thank you so much!!

Answer 18

Welcome :)
Special thanks to @.Sam.

Answer 19

yes, thank you to @.Sam.