Basic Algebra/Introduction to Basic Algebra Ideas/Exponents and Powers

Vocabulary

 * Exponent: A number written in superscript that denotes how many times the base will be multiplied by itself.
 * Base (or radix): The number to be multiplied by itself.

Example: $$5^2=25$$

In this example, the base is 5 and the exponent is 2.

Lesson
We use exponents to show when we're multiplying the same number more than one time.


 * $$ 3 \times 3 = 3^{2}$$
 * Three times three equals three to the second power (or three squared)


 * $$3 \times 3 \times 3 = 3^{3}$$
 * Three times three times three equals three to the third power (or three cubed)


 * $$3\times3\times3\times3= 3^{4}$$
 * Three times three times three times three equal three to the fourth power


 * $$2\times2\times2 = 2^{3}$$
 * Two times two times two equals two to the third power

Note that any nonzero number raised to the 0 power is always equal to 1.


 * $$2^{0} = 1$$
 * Two to the zero power equals one

We can also raise any number to a negative exponent. This is called the inverse exponent and places the number on the bottom of a fraction with a 1 on top:


 * $$2^{-2} = \frac{1}{2^{2}} = \frac{1}{4}$$
 * Two to the negative two equals one over two to the second power

Example Problems
Let's evaluate these expressions.


 * $$7^{2}$$
 * Seven to the second power equals forty-nine.


 * What is the area of a square with a side of 3 meters length?
 * So, the area of a square with a side length of 3 meters is 9 square meters.


 * $$c^{2}$$ where $$c = 6$$
 * So, c squared is 36.


 * $$x^{3}$$ where $$x = 10$$.
 * So, x to the third power is 1000.


 * $$y^{4}$$ where $$y = 2$$
 * So, y to the fourth is 16.


 * $$3^{-3}$$
 * So, three to the negative third power equals one twenty-seventh.

Practice Games

 * http://www.math.com/school/subject2/practice/S2U2L2/S2U2L2Pract.html
 * http://www.quia.com/pop/50485.html (scientific notation)
 * http://www.softschools.com/math/games/exponents_practice.jsp
 * http://www.quia.com/quiz/358716.html (King Kong Scientific Notation)
 * http://www.shodor.org/interactivate/activities/OrderOfOperationsFou/ (order of operations including exponents)

Practice Problems
Use  as the fraction line!  {Evaluate the following expressions:}

{ $$6^{2}=$${ 36_5 }
 * type="{}"}

{ $$2^{3}=$${ 8_5 }
 * type="{}"}

{ $$4^{2}=$${ 16_5 }
 * type="{}"}

{ $$5^{3}=$${ 125_5 }
 * type="{}"}

{ $$2^{4}=$${ 16_5 }
 * type="{}"}

{ $$9^{2}=$${ 81_5 }
 * type="{}"}

{ $$8^{2}=$${ 64_5 }
 * type="{}"}

{ $$5^{-3}=$${ 1/125|0.008_5 }
 * type="{}"}

{ $$6^{0}=$${ 1_5 }
 * type="{}"}

{ $$7^{2}=$${ 49_5 }
 * type="{}"}

{ $$12^{2}=$${ 144_5 }
 * type="{}"}

{ $$2^{4}=$${ 16_5 }
 * type="{}"}