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Simplifying Radicals

. . .

Fractional Exponents & Roots



Math - Fractional Exponents & Radicals

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.

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

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Math - Simplifying Radical Expressions - 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
- simplifying radicals -

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

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




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

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
- simplifying radicals -

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
- simplifying radicals -

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 of factors with decimal exponents: Math - Decimal Exponent - Multiplication - Initial Problem - example 7
- simplifying radicals -

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
- simplifying radicals -

Math - Decimal Exponent - Division - example 8

The final answer is: Math - Decimal Exponent - Division - Final Answer - example 8