Simplifying Radicals . . . FRACTIONAL EXPONENTS & ROOTS . . .

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Simplifying Radicals
. . .
Fractional Exponents & Roots

Simplifying Radicals & Roots - FRACTIONAL
EXPONENTS & ROOTS . . . Fractional Exponents - Exponents & Roots:

$Math Symbols - Fractional Exponent highlighted$ 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") :

$Math Symbols - Fractional Exponent - numerator highlighted$ 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 .

$Math Symbols - Fractional Exponent - denominator highlighted$ Denominator of the fractional

exponent (shown as "b")
The denominator of the fractional exponent is the root $Math Symbols - Root Symbol$ :

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

$Return to Exponents, Radicals, & Roots Page$ $Return to Exponents, Radicals, & Roots Page$ $Return to Exponents, Radicals, & Roots Page$ Return To "Exponents, Radicals, & Roots" click here

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

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$Simplifying Radicals - Math - Radicals - adding and subtracting$

Adding & Subtracting
Radicals

$Math - Multiplying Radicals$

Multiplying Radicals

$Math - Dividing Radicals$

Dividing Radicals

$Math - Rationalizing the Denominator$

Rationalize the
Denominator

$Math - Fractional Exponents & Radicals$

Fractional Powers & Radicals

$Math - Simplifying Radicals$

Simplifying "Radicals"

$Math - Calculate Square Root Without Using a Calculator$

Calculate Square Root
Without Using a Calculator

$Math - Calculate Roots Using Equations$

Calculate Roots
Using Equations

$Math - Free Videos on Radicals & Roots + Free Resources$

Videos
& Free Resources

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FRACTIONAL EXPONENTS & ROOTS

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

$Math - Fractional Exponent - Compute the Exponent First - example 1$ Compute the exponent first: $Math - Fractional Exponent - Compute the Exponent First - Initial Problem - example 1$
- simplifying radicals -

$Math - Fractional Exponent - Compute the Exponent First - example 1$

The final answer is: $Math - Fractional Exponent - Compute the Exponent First - Final Answer - example 1$

$Math - Fractional Exponent - Compute the Square Root First - example 2$ Compute the square root first: $Math - Fractional Exponent - Compute the Square Root First - Initial Problem - example 2$
- simplifying radicals -

$Math - Fractional Exponent - Compute the Square Root First - example 2$

The final answer is: $Math - Fractional Exponent - Compute the Square Root First - Final Answer - example 2$

$Math - Fractional Exponent using variable - Compute the Exponent First - example 3$ Compute the exponent first: $Math - Fractional Exponent using variable - Compute the Exponent First - Initial Problem - example 3$

$Math - Fractional Exponent using variable - Compute the Exponent First - example 3$

The final answer is: $Math - Fractional Exponent using variable - Compute the Exponent First - final answer - example 3$

$Math - Fractional Exponent - Compute the Square Root First - example 2$ Compute the square root first: $Math - Fractional Exponent using variable - Compute the Square Root First - Initial Problem - example 4$

$Math - Fractional Exponent using variable - Compute the Square Root First - example 4$

The final answer is: $Math - Fractional Exponent using variable - Compute the Square Root First - final answer - example 4$

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

$Math - Fractional Exponent - Multiplication - example 5$ Multiplication with fractional exponents: $Math - Fractional Exponent - Multiplication - Initial Problem - example 5$

$Math - Fractional Exponent - Multiplication - example 5$

The final answer is: $Math - Fractional Exponent - Multiplication - Final Answer - example 5$

$Math - Fractional Exponent - Division - example 6$ Dividing factors with fractional exponents: $Math - Fractional Exponent - Division - Initial Problem - example 6$

$Math - Fractional Exponent - Division - example 6$

The final answer is: $Math - Fractional Exponent - Division - Final Answer - example 6$

$Math - Decimal Exponent - Multiplication - example 7$ Multiplication with decimal exponents: $Math - Decimal Exponent - Multiplication - Initial Problem - example 7$

$Math - Decimal Exponent - Multiplication - example 7$

The final answer is: $Math - Decimal Exponent - Multiplication - Final Answer - example 7$

$Math - Decimal Exponent - Division - example 8$ Dividing factors with decimal exponents: $Math - Decimal Exponent - Division - Initial Problem - example 8$