EVALUATING THIS RATIONAL EXPONENT PROBLEM

[divagirl5000]

the problem says "evaluate 5 to the root of 1540 to three decimal places using a calculator."

i'm not sure what i'm supposed to do here..
thank you for any help.
:]

 

[pka]

I have a very poor knowledge of the capabilities of calculators.
Having said that there are two standard ways to evaluate these numbers
\(\displaystyle \L
5^{\left( {\frac{1}{{1540}}} \right)}\) or \(\displaystyle \L
e^{\left( {\frac{{\ln (5)}}{{1540}}} \right)}\).

My computer algebra system gave the same answer for these to methods.

 

[soroban]

Hello, divagirl5000!

I have a different interpretation . . . can you clarify?

The problem says "Evaluate 5 to the root of 1540 to three decimal places using a calculator."

I read it as: \(\displaystyle \L\,5^{{^{\sqrt{1540}}}\)

Or did you mean "the 1540^th root of 5" ?

 

[divagirl5000]

thank you both of you!!!

yes, that is correct when you asked me to clarify what you read it as..having said that does that change the answer given in the first reply?

thankyou very much both of you
:]