## 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

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Compute the exponent first:

Compute the square root first:

Compute the exponent first:

Compute the square root first:

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:

Dividing factors with fractional exponents:

Multiplication of factors with decimal exponents:

Dividing factors with decimal exponents: