- When multiplying two bases of the same value, keep the bases the
same and then add the exponents together to get the solution.
5
1
𝑏3 ⋅ 𝑏3
5
1
= 𝑏3 + 3
=𝑏
1
1
1
= 33 + 2
5+1
3
=3
6
= 𝑏3
1
55 ⋅ 55
3
1
= 55 + 5
2+3
6
=5
𝟓
𝟔
= 𝟓𝟓
=𝟑
= b2
3
1
33 ⋅ 32
3+1
5
𝟒
- When you are dividing terms that have the same base, just
subtract their exponents to find your answer.
2
3
43
1
=4
4
87
𝑎5
1
2
43
𝑎5
87
2 1
−
3 3
3 1
−
5 5
4 2
−
7 7
𝟏
= 𝟒𝟑
7
= 36
=𝑎
𝟐
= 𝒂𝟓
7
= 36
=8
𝟐
= 𝟖𝟕
7
= 36
- If a power is being raised to another power, multiply the
exponents and leave the base the same.
1
1 2
(53 )
1
1
3
2
=5( ⠂ )
1
2 3
(23 )
= 51/6
2
1 5
(95 )
1
2
5
5
=2( ⠂ )
=9( ⠂ )
= 22/9
= 92/25
2
1
3
3
- When any base is being multiplied by an
exponent, distribute the exponent to each part of the base.
2
(𝑥𝑦)3
𝟐
𝟑
𝟐
𝟑
=𝒙 𝒚
1
(25⠂9)2
1
(27⠂8)3
1
2
1
3
= 25 ⠂9
1
2
= 27 ⠂8
= 5⠂3
= 3⠂2
= 𝟏𝟓
=𝟔
1
3
- The power of a quotient is equal to the quotient obtained when the
numerator and denominator are each raised to the indicated
power separately, before the division is performed.
=
2
83
2
273
1
2
2
8 3
( )
27
=
=
(23 )3
2
(33 )3
4 2
( )
16
27 3
( )
8
4
=
1
=
𝟒
=
1
1
2
𝟗
=
42
=
1
162
(33 )3
1
(23 )3
1
𝟏
=
𝟐
1
(22 )2
273
1
83
=
𝟑
𝟐
1
(4 2 )2
- Any base with an exponent of zero is equal to one.
a0 = 1
𝑎 0
( )
𝑏
20 = 1
= 1
- A number with a negative exponent should be put to the
denominator, and vice versa.
8
=
=
=
2
−3
27
1
2
1
(8 ⁄3 )
1
=
=
22
𝟏
𝟒
=
1
−3
1
1
27 ⁄3
4
=
1
31
=
𝟏
𝟑
=
3
−2
1
3
1
(4 ⁄2 )
1
23
𝟏
𝟖
- When changing expressions from exponential form to radical
form, write the radical sign, copy the base it becomes the
radicand, and exponent in the numerator becomes the power of
the radicand and the exponent in the denominator becomes the
index.
b3/5
52/3
=
𝟓
𝟑
= √𝒃𝟑
√𝟓𝟐
(x3y2)3/4
𝟒
= √(𝒙𝟑 𝒚𝟐 )𝟑
- When changing radical expression to exponential form, copy the
radicand, it becomes the base now, the power becomes exponent
in the numerator, and the index becomes the denominator of the
rational exponent.
5
15 √𝑏 3
= 15b3/5
3
30 √𝑎2
= 30a2/3
5
√𝑎4
= a4/5