### Home > PC > Chapter 3 > Lesson 3.1.1 > Problem 3-9

THE MEANING OF DECIMAL EXPONENTS

Express

as a fraction, and rewrite using this fraction. We can use the power law for exponents to break up this fraction into two factors. Find the value of

so that. Rewrite your answer to part (b) as a certain root of

raised to a certain power by copying and filling in the blanks of: . Why is it generally better to take the root first, especially when you're working without a calculator?

The numbers remain smaller and therefore easier to work with.

Do the calculation on your graphing calculator.

Now calculate

. How does this answer compare with the previous one? Reshma notices that the answer for

is close to . Kahlil knows she could get closer by using more decimal places in the exponent. Use guess and check to find (to the nearest) so that as possible. In a flash of brilliance, Reshma suddenly knows how to get several more decimal places instantly. What keys can she press on her calculator to do this?

She can rewrite

as , then calculate gives several more decimal places instantly.