Title: Lesson 1–1
Author: Teri Willard
Last saved by: Glencoe Mathematics

Lesson 7–6

Example 1  Radical and Exponential Forms
a. Write  in radical form. | b. Write  in radical form.
=  Definition of | =  Definition of

Example 2  Evaluate Expressions with Rational Exponents
Evaluate each expression.
a. |
Method 1 | Method 2
=      b^–n = | =        729 = 3^6
=      = | =         Power of a Power
=       729 = 3^6 | = 3^–1              Multiply exponents.
=           Simplify. | =                3^–1 =
b. |
Method 1 | Method 2
=           Factor. | =       343 = 7^3
=          Power of a Power | =         Power of a Power
= | = 7^2              Multiply exponents.
=          343 = 7^3 | = 49             7^2 = 49
=     Expand the square. |
= 7 • 7 or 49     Find the cube root. |

Example 3  Rational Exponent with Numerator other than 1
SPORTS The volume of the basketball most commonly used in youth basketball leagues is 121.5π cubic inches. The formula for the volume of a sphere, where r is the radius, is V = πr^3 and the formula for the surface area is A = 4πr^2. What is the surface area of the youth–size basketball? Leave the answer in terms of π.  
You are given the volume of the basketball. If you can find the value of r^3, then  can be used in the formula for surface area. (The cube root of r^3 squared will be r^2.) Substitute the known value for V into the formula V = πr^3 and solve for r^3. Then substitute  for r^2 into the formula for surface area.

V = πr^3	Formula for volume
121.5π = πr^3	Substitute 121.5π for V.
r^3 = (121.5)	Divide both sides by π and then multiply by .
r^3 = 91.125	Simplify.

A = 4πr^2		Formula for surface area.
= 4π		The cube root of 91.125 is the radius and the formula uses r^2.
= 4π(20.25)		Use a calculator.
= 81π

The surface area of the basketball is 81π in.^2

Example 4  Simplify Expressions with Rational Exponents
Simplify each expression.
a. | b.
= 	Multiply powers. | = 	b^–n =
= 	Add exponents. | =  •
= 11	  = 11 | = 	 =
| = 	 = m^1 or m

Example 5  Simplify Radical Expressions
Simplify each expression.
a. | b.
=                  Rational exponents | =
=                 1024 = 2^10, 32 = 2^5 | =
=                      Power of a power | =  •
=                  Quotient of Powers | =
=  or          Simplify. | =  or

Example 6  Simplify Radical Expressions
If y is a positive number, then = ?
A. 
B. 
C.
D. 

 = 	Add the exponents in the numerator.
	= y y	Quotient of Powers
	= y	The answer is B.