# Thread: [SOLVED] how do I do exponents that are negative decimals?

1. ## [SOLVED] how do I do exponents that are negative decimals?

such as q = 5^-.5

If I were allowed to use a calculator with the y^x key I'd be fine but only standard calculators or pen/paper for the test (managerial economics). so if someone could show me how to do this on paper or just by using a standard calculator that would be great. thanks

2. Originally Posted by Meghiddo
such as q = 5^-.5

If I were allowed to use a calculator with the y^x key I'd be fine but only standard calculators or pen/paper for the test (managerial economics). so if someone could show me how to do this on paper or just by using a standard calculator that would be great. thanks
You are supposed to know a few rules and laws concerning calculations of powers:

$a^{-n} = \frac1{a^n}$ that means the negative sign of an exponent can be translated into a fraction with the numerator 1.

$a^{\frac1n} = \sqrt[n]{a}$ that means a fraction as exponent can be translated into a root. (Jhevon published recently a very impressive image about the (flower)power and it's root. Search for it)

$5^{-\frac12} = \frac1{5^{\frac12}} = \frac1{\sqrt{5}}$