# Exponents

• Jan 11th 2010, 08:36 PM
Veronica1999
Exponents
What is 5 raised to the 2.5 power?

Veronica.
• Jan 11th 2010, 08:44 PM
Jhevon
Quote:

Originally Posted by Veronica1999
What is 5 raised to the 2.5 power?

Veronica.

Just plug it into your calculator: $\displaystyle 5^{2.5} \approx 55.902$ to 3 d.p. is that what you want?
• Jan 11th 2010, 08:50 PM
Veronica1999
Can I get the answer without using a calculator?
• Jan 11th 2010, 08:56 PM
Jhevon
Quote:

Originally Posted by Veronica1999
Can I get the answer without using a calculator?

not exactly. you could write it using radicals for the exact answer. that would be $\displaystyle 5^{2.5} = 5^{5/2} = \sqrt {5^5} = \sqrt {3125}$

otherwise, you could get a decimal approximation by hand. but that is way more work than this is worth, and i doubt your professor would want you to do that
• Jan 12th 2010, 01:05 AM
aidan
Quote:

Originally Posted by Veronica1999
What is 5 raised to the 2.5 power?

Veronica.

$\displaystyle 5^{2.5} = 5^2 \cdot 5^{0.5}$

$\displaystyle 25 \sqrt{5}$

You should be able to extract the $\displaystyle \sqrt{5}$ w/o a calculator if that part is required.
• Jan 12th 2010, 01:23 AM
BabyMilo
you could use Binomial Expansion.