Exponents and Radicals

By M Bourne

√(a + b)¹⁰

Exponents are a very important part of algebra. An exponent is just a convenient way of writing repeated multiplications of the same number.

Radicals involve the use of the radical sign, `sqrt(\ )`. Sometimes these are called surds.

If you learn the rules for exponents and radicals, then your enjoyment of mathematics will surely increase! (Yeah, right... :-)

The Binomial Theorem, which shows how to expand expressions like (x + y)⁶.

Exponential and Logarithmic Functions, which talks about applications of expressions like `10^x` and log x.

Differentiation of polynomials, where one of the steps involves exponents.

Roots and radicals, from the basic algebra section.

In this Chapter

1. Simplifying Expressions with Integral Exponents - defines exponents and shows how to use them when multiplying or dividing in algebra.

2. Fractional Exponents - shows how an fractional exponent means a root of a number

3. Simplest Radical Form - this technique can be useful when simplifying algebra

4. Addition and Subtraction of Radicals - shows how to add or subtract expressions involving the square root sign

5. Multiplication and Division of Radicals (Rationalizing the Denominator) - while this method is not as important as it was in the pre-calculator days, it is still a useful technique