# Laws of Rational Exponents Worksheets

What are the Laws Rational Exponents? To solve mathematical problems with integers as exponents, you use specific rules. However, when it comes to problems that involve numbers with rational exponents, you can start freaking out. It may seem challenging, but if you take a deep breath, you will know that it is not that hard. Did you know that the rules for multiplying and dividing exponents also apply to rational exponents? Before we start learning the laws, you need to understand what rational exponents mean. a(1/n) = n√a a(m/n) = n √(am. Zero-exponent Rule: anything raised to the power zero equals one. [a0 = 1] Power-Rule: you have to multiply the exponents when power is raising a power. [(a (1/m)) (1/n) = a(1/mn) = mn√a] Product Rule: When the same bases are multiplied with different exponents, you can simply add the exponents. [a(1/m) × a(1/n) = a(1/m+1/n)] Quotient Rule: When the same bases are being divided with different exponents, you can simply subtract the exponents. [a(1/m) ÷ a(1/n) = a(1/m - 1/n)]

• ### Basic Lesson

Demonstrates general rules of simplifying radical expressions.

• ### Intermediate Lesson

Explores how to convert various fractional powers within an expression.

• ### Independent Practice 1

Contains 20 Laws of Rational Exponents problems. The answers can be found below.

• ### Independent Practice 2

>Features another 20 Laws of Rational Exponents problems.

• ### Homework Worksheet

Laws of Rational Exponents problems for students to work on at home. Example problems are provided and explained.

• ### Topic Quiz

10 Laws of Rational Exponents problems. A math scoring matrix is included.

• ### Homework and Quiz Answer Key

Answers for the homework and quiz.

• ### Lesson and Practice Answer Key

Answers for both lessons and both practice sheets.

#### Fun Fact:

What inspired Einstein and his mathematical brilliance? It is reported that when a young Einstein was only five years old, his father gave him a compass to entertain him. Intrigued by the fact that whichever way he pointed the device the needle always pointed in the same direction, he began to wonder if there was some invisible force directly it. That simple childhood question turned into a lifelong mission as Einstein developed his masterful mind in the years to come.