1. Simplify each expression:
Warm Up
Simplify each expression:

2. Math 8H
Fractional Exponents
Algebra Glencoe McGraw-Hill JoAnn Evans

3. You know how to raise a number to a power
You know how to raise a number to a power. For example, to square a number you use that number as a factor two times.
The inverse operation of squaring a number is finding the square root.
Square roots are written with a radical symbol that resembles a check mark.

4. index
The index is a small number that sits on the “check mark” part of the radical symbol.
radicand
Radicals with an index of 2 are called SQUARE ROOTS. They’re so common that we normally leave off the index number. A radical without an index number is ASSUMED to be a square root.

5. Radicals with an index of 3 are called CUBE ROOTS.
What number used as a factor 3 times is equal to 8?

6. An index can be any natural number; but only radicals with an index of 2 (square roots) and with an index of 3 (cube roots) have special names.

7. Radicals can be expressed without a radical sign by using fractional exponents.
The index of the radical expression becomes the denominator of the fractional exponent.
The exponent of the radical expression becomes the numerator of the fractional exponent.

8. Change from a fractional exponent to radical notation.1 2
Write the base of the fractional exponent as the radicand.
The denominator of the fractional exponent is the index. 1 3
The numerator of the fractional exponent is the exponent outside the parentheses. 1 4

9. A fractional exponent doesn’t have to have a numerator of 1.
Other fractions like and can create more complicated radical expressions.
Rule #6 for exponents says:

10. To evaluate an expression with a rational exponent, first change it into a radical expression.
Then follow the order of operations. Simplify within the parentheses first, then raise that answer to the power outside the parentheses. 1 2 3 2 2 3 5 3

11. All other rules for exponents also apply to rational exponents.

12. Can you think of an easier way to do this problem?