Download EXPONENTS

If a number is in exponential form, the
exponent represents how many times the
base is to be used as a factor. A number
produced by raising a base to an
exponent is called a power. Both 27 and
33 represent the same power.
Exponent
Base
2
7
Exponential form-a number written with a
base and an exponent
Exponent-shows how many times the base
number is going to be multiplied
Base- the number that is used as a factor
Power- A number produced by raising a
base to an exponent.
Writing as an EXPONENT
Write in exponential form...
A. 4 • 4 • 4 • 4
4 • 4 • 4 • 4 = 44
Identify how many
times 4 is a factor.
B. (–6) • (–6) • (–6)
(–6) • (–6) • (–6) = (–6)3
Identify how many
times –6 is a factor.
Reading Math
Read –(63) as “-6 to the 3rd power or -6 cubed”.
Evaluate.
Find the product of five 3’s.
A. 35
35 = 3 • 3 • 3 • 3 • 3
= 243
B. (–3)5
Find the product of five –3’s.
(–3)5 = (–3) • (–3) • (–3) • (–3) • (–3)
= –243
Helpful Hint
Always use parentheses to raise a negative number to a
power.
Multiply
Exponent of
Exponent
Divide
Negative
Exponent
Add
the exponents
Keep the same base
2
3 x
3
3 =
2+3
3 =
5
3
Multiply: Write the product as
one power
x5 • y2
x5 • y2
412 • 417
2+7
41
419
Cannot combine; the
bases are not the same.
Add exponents.
 Subtract
the exponents
 Keep the same base
6
3 =
2
3
6-2
3 =
4
3
Divide. Write the quotient as one power.
A.
5
7
3
7
75 – 3
7
B.
Subtract exponents.
2
10
x
9
x
x10 – 9
x
Subtract exponents.
Think: x1 = x
 Keep
the same base
 Multiply the exponents
2
3
(3 ) =
2x3
3 =
6
3
Simplify.
Simplify.
A. (54)2
2
3
C.
12 –3
(54)2
= 54 • 2
=
58
Multiply exponents.
=
=
2
3
12 • –3
2 –36
3
 Put
one over that number with
a positive exponent
-2
3
= 1= 1
2
3 9
A negative exponent means divide,
because the opposite of multiplying is
dividing
 Whenever you have an exponent that is
negative, make it its reciprocal (Flip it!)
and remove the sign.

4-3
=
4-3
1
=
1
43
1
6-2
=
62
1
= 62 = 36
If a base other than zero is raised to a
zero power it ALWAYS equals one.
 50= 1
 7380 =1


If zero is raised to a zero power it ALWAYS
equals zero.

Anything raised to a power of 1 is itself
because that shows that there is 1 of the
base.

51= 5

X1= x

Find the power of each factor and
multiply.

(6x)3= 63x3= 216x3

(xy)4= x4y4

(x/y)3= x3/y3
Evaluate: 5 – (6 – 4) -3 + (-2) 0
Do it on your own!
When you…
2
3 x
3
3 =
2+3
5
3 =3
6
3 =
2
3
6-2
3 =
4
3
2
3
(3 ) =
2x3
3 =
6
3
-2
3
= 1= 1
2
3 9
Multiply- Add exponents
Divide - Subtract exponents
 Exponent
to Exponent- Multiply
 Negative Exponents- Make
the reciprocal