  home adding and subtracting fractions removing brackets 1 comparing fractions complex fractions decimals notes on the difference of 2 squares dividing fractions solving equations equivalent fractions exponents and roots factoring rules factoring polynomials factoring trinomials finding the least common multiples the meaning of fractions changing fractions to decimals graphing linear equations inequalities linear equations linear inequalities multiplying and dividing fractions multiplying fractions multiplying polynomials percents polynomials powers powers and roots quadratic equations quadratic expressions radicals rational expressions inequalities with fractions rationalizing denominators reducing fractions to lowest terms roots roots or radicals simplifying complex fractions simplifying fractions solving simple equations solving linear equations solving quadratic equations solving radical equations in one variable solving systems of equations using substitution straight lines subtracting fractions systems of linear equations trinomial squares
Try the Free Math Solver or Scroll down to Tutorials!

 Depdendent Variable

 Number of equations to solve: 23456789
 Equ. #1:
 Equ. #2:

 Equ. #3:

 Equ. #4:

 Equ. #5:

 Equ. #6:

 Equ. #7:

 Equ. #8:

 Equ. #9:

 Solve for:

 Dependent Variable

 Number of inequalities to solve: 23456789
 Ineq. #1:
 Ineq. #2:

 Ineq. #3:

 Ineq. #4:

 Ineq. #5:

 Ineq. #6:

 Ineq. #7:

 Ineq. #8:

 Ineq. #9:

 Solve for:

 Please use this form if you would like to have this math solver on your website, free of charge. Name: Email: Your Website: Msg:

## Introduction

A power, or an exponent, is used to write a product of numbers very compactly. In this leaflet we remind you of how this is done, and state a number of rules, or laws, which can be used to simplify expressions involving indices.

## 1. Powers, or exponents

We write the expression 3×3×3×3 as We read this as "three to the power four". Similarly z × z × z = We read this as " z to the power three" or " z cube".

In the expression the exponent is c and the number b is called the base. Your calculator will probably have a button to evaluate powers of numbers. It may be marked . Check this, and then use your calculator to verify that Exercises

1. Without using a calculator work out the value of 2. Write the following expressions more concisely by using powers.  ## 2. The laws of exponents

To manipulate expressions involving exponents we use rules known as the laws of exponents. The laws should be used precisely as they are stated - do not be tempted to make up variations of your own! The three most important laws are given here:

First law When expressions with the same base are multiplied, the exponents are added.

Example

We can write You could verify this by evaluating both sides separately.

Example Second Law When expressions with the same base are divided, the exponents are subtracted.

Example

We can write Third law Note that m and n have been multiplied to yield the new exponent mn.

Example

It will also be useful to note the following important results: Exercises

1. In each case choose an appropriate law to simplify the expression: 2. Use one of the laws to simplify, if possible,  