An exponent as decimal , how it will be ..?

[robinphilip01]

Hi,

What is 10ᶺ0.2 ? can you please explain this ..?
weather it can be expressed like that ?
( my steps:
10ᶺ2/10
10ᶺ2*10ᶺ-1 ..... ?)

[n00bpron00bpron00b]

I think it should be

(10)^0.2 = (10)^(2/10) = (10)^(1/5) = 5th root of 10 the whole raised to 1 = 5th root of 10

[tommywallach]

Hey Robin,

Noob is right. ALSO, be very careful, because your attempted rephrase betrays a fundamental problem with the basic exponent rule

x ^ y * x ^ z = x ^ (y+z)

In your version, this becomes x ^ y * x ^ z = x ^ (y * z), which is incorrect.

(Technically, you did it through DIVISION, but it's the same error. You would SUBTRACT the powers, not divide them).

10ᶺ2 / 10^1 does not equal 10^.2, because we don't divide the powers, we subtract them.

-t

[robinphilip01]

Thank you Tommy,Thank you Noob !!

[tommywallach]

Glad to help!

-t