### Concept (1)

The rules for multiplying and dividing exponents apply to rational exponents as well - however the operations will be slightly more complicated because of the fractions. Some basic rational exponent rules apply for standard operations. When multiplying exponents, we add them. When dividing exponents, we subtract them. When raising an exponent to an exponent, we multiply them. If the problem has root symbols, we change them into rational exponents first.

### Sample Problems (7)

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Simplify:

 8¼ 8⅔
###### Problem 1
How to simplify a product or quotient using fractional exponents.

Simplify:

 ( x½y⅔ )¹² x
###### Problem 2
How to simplify an expression using rational exponents.

Simplify:

 √ x⁵y⁻² x⁻⁴∛y
###### Problem 3
How to simplify an expression with radicals and rational exponents.

Simplify:

⁶√x⁵(⁶√x + ⁶√x⁷)
###### Problem 4
How to simplify a product of radicals using rational exponents.
###### Problem 5
Simplifying exponents with a power to a power.
###### Problem 6
Multiplication and division rules for rational exponents.
###### Problem 7
Simplifying expressions with embedded radical roots.