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Workbook

EXPONENTIAL EXPRESSIONS

OBJECTIVES

✓ Solve the equations with exponents.
✓ Explains rational powers of real numbers. Shows the properties of radicals by
using rules for exponents

EXPONENTIAL EXPRESSIONS

When a number is multiplied by itself a specific number of times, it is said to be raised to a power.

a  bwhere a is the base, nis the exponent or power that indicates the number of times the base is
n
n
to be multiplied by itself, and b is the product of this multiplication. The expression a is called “a to
the power of n”.

2
9
In the expression3 , 3 is the base and 2 is the exponent. This means that 3.3  .
2 times
Rules of Exponents:

1) If x and m  , then x x x x .............. x x      m and x x x .......... x m x     
mtimes mtimes

2) x  0 1 x 0 (ZeroExponent)
x  1
1

x  x.x
2

x  x.x.x
3
x 
n
x.x.x......x

ntimes
3) ( 1) n  1 if nis an even integer.

( 1) n   1 if nis an odd integer.

0
REMARK: 0 is indeterminate.

Example 1: Evaluate each expression given below.

a) 2 3 

3
b) 2  

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