## Simplifying Radicals. . .Fractional Exponents & Roots

Simplifying Radicals & Roots - FRACTIONAL EXPONENTS & ROOTS . . .

Fractional Exponents - Exponents & Roots :

The fractional exponent notation represents
both an exponent and a root (two mathematical operations)
as the two parts of a fraction (shown above as "a" and "b") :

• Numerator of the

fractional exponent (shown as "a")

The numerator of the fractional exponent is the exponent. It shows how many times the base (shown as "Z") will be multiplied by itself.
• Denominator of the

fractional exponent (shown as "b")
The denominator of the fractional exponent is the root :

b = 2 (square root), b = 3 (cube root), b = 4 (4th root), b = 5 (5th root), etc.

The Properties of Radicals & Roots - Real Numbers - click description

The Exponent and the Root can be evaluated in either order with exactly the same result

"Top of Page"

Compute the exponent first:

- simplifying radicals -

The final answer is:

Compute the square root first:

- simplifying radicals -

The final answer is:

Compute the exponent first:
- simplifying radicals -

The final answer is:

Compute the square root first:
- simplifying radicals -

The final answer is:

The Rules of Multiplication and Division for fractional exponents and decimal exponents are exactly the same rules used with non-fractional exponents

Multiplication with fractional exponents:
- simplifying radicals -

The final answer is:

Dividing factors with fractional exponents:
- simplifying radicals -

The final answer is:

Multiplication of factors with decimal exponents:
- simplifying radicals -

The final answer is:

Dividing factors with decimal exponents:
- simplifying radicals -

The final answer is: