### Home > PC3 > Chapter 5 > Lesson 5.2.2 > Problem 5-65

THE MEANING OF DECIMAL EXPONENTS

Express

as a fraction, and rewrite using this fraction. The power property of exponents can be used to break up this fraction into two factors. Write the value of

so that. Solve:

Rewrite your answer to part (b) as a 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 are working without a calculator?

The numbers remain smaller and therefore easier to work with.

Use a calculator to evaluate your expression from part (c).

Now calculate

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

is close to . Kahlil knows she can get a value closer to by using more decimal places in the exponent. Use guess and check to determine (to the nearest) so that is as close to as possible. Since

is slightly larger than , choose an exponent a little less than . 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?

Rewrite

using a logarithm.