applying exponential properties to (e^(x^b))^2

[ignacio28]

Hi,

Sorry for the silly question, but I have a doubt about applying the exp properties to:

(e^(x^b))^2

I think it would be equal to

e^(x^2b)

Is that ok?

Thank you

 

[lev888]

(e^(x^b))^2 = (e^(x^b)) * (e^(x^b)) = ?
Hint: x^a * x^b = ?

 

[Steven G]

Hi,

Sorry for the silly question, but I have a doubt about applying the exp properties to:

(e^(x^b))^2

I think it would be equal to

e^(x^2b)

Is that ok?

Thank you

Consider this, you have 5^8 and you want to square this. Now the power of 5 (before squaring) is 8. So [5^8]^2 = 5^16.

But what if we want to think of 8 as 2^3. That is instead of writing 5^8 we want to write it as 5^{(2^3)}. Note that the power of 8 IS 2^3. Now consider (5^{(2^3)})². This will NOT be 5^{(2^6)}= 5⁶⁴. It will be 5^{(2^3)*2} = 5^8*2 = 5¹⁶, which is the original and correct answer.

 

[ignacio28]

So, the correct answer is

e^((x^b)*2)

Thank you!