1 7.4 Rational Exponents

2 Some exponent problems that you already know how to do: If a cube root were an exponent, what exponent would it have to be? A fraction as an exponent, but how can that be???

3 Why do we need fractional (rational) exponents? If you have $100 a bank account that pays 5% interest per year, After one year, your account balance is: $ After two years, your account balance is: $ After three years, your account balance is: $ Conclusion: In this situation, the exponent represents the number of years that the money is in the bank.

4 Why do we need fractional (rational) exponents? Using the same situation as before: If you have $100 a bank account that pays 5% interest per year, After one half year, your account balance is: $ After two and a half years, your account balance is: $ After seventeen months, your account balance is: $ It is way too simplistic to assume that the money will be in the bank for whole years all the time.

5 Some simple fractional exponents… A square root is the same as the one half power:A cube root is the same as the one third power:A fourth root is the same as the one fourth power:A fifth root is the same as the one fifth power: And so on and so forth…

6 Simplify these fractional exponent expressions

7 Some slightly more difficult fractional exponent expressions

8 Using other fractions as exponents: If the nth root of a is a real number and m is an integer, then In other words, use the denominator of the fraction first to find the n th root (as before), then raise the result to the m th power. Examples:

9 Using other fractions as exponents:

10 Using other fractions as exponents:

11 Using other fractions as exponents:

12 Using other fractions as exponents:

13 Operations with Fractional Exponents

14 Operations with Fractional Exponents

15 Write the following expressions using rational exponents.