Rules for Rational Exponents - Concept

Concept 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 Sample Problems (7)

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Rules for Rational Exponents - Problem 1

Simplify:

8¼
8
Problem 1
How to simplify a product or quotient using fractional exponents.
Rules for Rational Exponents - Problem 2

Simplify:

( x½y )¹²
x
Problem 2
How to simplify an expression using rational exponents.
Rules for Rational Exponents - Problem 3

Simplify:

x⁵y⁻²
x⁻⁴∛y
Problem 3
How to simplify an expression with radicals and rational exponents.
Rules for Rational Exponents - Problem 4

Simplify:

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