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Exponet
EXAMPLES & SOLUTIONS
Expressions: Exponents
Exponents are numbers that tells the base number how many times to multiply itself by.
The number above the base of a number is called the exponent.
The exponent tells the number of times the base will be multiplied.
Exponents are often needed to express very large or small numbers.
Exponents can be expressed in many ways.
There are many rules in solving exponent expressions.
EXPONENT PROPERTY
Rules of exponents
Rule:
x
n
where x = base, n = exponent
base
exponent
n
X
x * x * x * x . . . x
}
power
}
factors
"x" raised to the power of "n"
OR
x to the "n" power
Exponents
Examples of evaluating exponent expressions
3
4
= (4 *4 * 4 )
"4" is raised to the power of "3"
This means that 4 is multiplied by itself 3 times.
1
4
=
4
2
=
4
4 * 4 = 16
3
=
4
16 * 4 = 64
4
5
= (5 * 5 * 5 * 5 )
5" is raised to the power of "4"
This means that 5 is multiplied by itself 5 times.
1
5
=
5
2
=
5
5 * 5 = 25
3
=
5
25 * 5 = 125
4
=
5
125 * 5 = 625
3
-2
= (-2 * -2 * -2)
-2" is raised to the power of "3"
This means that -2 is multiplied by itself 3 times.
1
-2
=
-2
2
=
-2
-2 * -2 = 4
3
=
-2
4 * -2 = -8
EXPLANATION OF EXPONENT RULES
Product Exponent Rule:
*
x
n
x
m
=
x
m + n
Power of Product Rule:
( )
x * y
m
=
x
m
*
m
y
2
*
3
=
2
2
=
2
2 * 3
2
6
2 * 3
( )
=
3
*
​2
3
3
3
Division Exponent Rule:
n
x
m
x
=
x
m - n
Power of Division Rule:
x
m
y
=
x
m
( )
m
y
=
3
2
2
2
3 - 2
2
=
1
2
2
=
3
3
( )
3
2
3
3
Addition Exponent Rule:
+
x
n
x
m
=
x
m * n
Power of the Power Rule:
( )
x
m
n
=
x
m * n
3
2
+
=
2
​2
=
2 + 3
2
5
2
=
1
3
2
( )
3 * 1
2
=
2
3
Negative Exponent Rule:
=
a
- n
1
n
a
Fractional Exponent Rule:
=
a
m
n
a
m
n
=
-3
2
1
2
3
Zero Exponent Rule:
if a = 0,
a
0
= 1
0
2
= 1
3
2
4
=
4
3
2
Exponent of One Rule:
= a
a
1
1
2
= 2
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