Question

What is the missing exponent?

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(2^-5) =2^-15

The missing exponent is in the brackets, I just need help finding it.

Answer 1

After this one, I have one more question if your willing to help out.

Answer 2

Say the missing exponent = x. Then... \[(2^{-5}) (x) = 2^{-15}\] we can find x by dividing the two given exponents. \(\dfrac{2^{-15}}{2^{-5}}\)

When dividing exponents, the powers subtract eachother. \(\dfrac{x^m}{x^{n}} = x^{m-n}\)

Answer 3

Do you see what I mean?

Answer 4

Sort of

Answer 5

Yea ok, I get it now

Answer 6

What did yu get as the missing exponent?

Answer 7

Okay. Lets solve for \(\dfrac{2^{-15}}{2^{-5}}\) first.
What is \(2^{-15+5} =~?\)

Answer 8

2^-10
also, how do you get the power of numbers without the ^

Answer 9

-15 + 5 = -20??

Answer 10

Yes, you are right, it is -5, but remember our rule? \(\large \dfrac{2^{-15}}{2^{-5}} = 2^{-15 -(-5)}= 2^{-15 + 5}\)

Answer 11

oh yea, so it is 2^-10 ok

Answer 12

Remember, 2 negatives make a positive :D

Answer 13

Mmhmm, it's 2\(^{-10}\)

Answer 14

So do you agree that if \(x=2^{-10}\), that \((2^{-5})(2^{-10}) = 2^{-15}\)?

Answer 15

Yes, so then in the blank, I would put 2^-10

Answer 16

Yes :D \(\checkmark\)

Answer 17

thanks