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

5-65.

​THE MEANING OF DECIMAL EXPONENTS  Homework Help ✎

  1. Express as a fraction, and rewrite using this fraction.

  2. The power property of exponents can be used to break up this fraction into two factors. Write the value of so that .

    Solve:

  3. Rewrite your answer to part (b) as a root of raised to a certain power by copying and filling in the blanks of .

  4. 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.

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

  6. Now calculate . How does this answer compare with the previous one?

  7. 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 .

  8. 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.