Indices Review 5.1 SACHS
Multiplication, ADD the Indices:
x12 × x4 = x
x7 × x2 = x
x5 × x3 = x
am × an = am+n
Multiplication, ADD the Indices:
Multiply the numbers, add the indices.
3y10 × 2y8 =    y
10x5 × 3x4 =    x
5a3 × 2a4 = 10a7
Multiplication, ADD the Indices:
2xy3 × 4x3y3 =    x   y
x2y2 × x3y5 = x   y
Put all those skills together....
Division, SUBTRACT the Indices:
c10 ÷ c4 = c
x5 ÷ x3 = x
y8 ÷ y6 = y
am ÷ an = am−n
Division, SUBTRACT the Indices:
Divide the numbers, subtract the indices.
10y10 ÷ 2y8 =    y
30x7 ÷ 10x2 =   x
6a5 ÷ 2a3 = 3a2
Division, SUBTRACT the Indices:
Put all those skills together....
15x4y11 ÷ 5xy7 =    x   y
x8y4 ÷ x3y2 = x   y
Power of powers,
MULTIPLY the indices.
(g2)10 = g
(x5)3 = x
(a1)7 = a
(am)n = am×n
Power of powers,
MULTIPLY the indices.
Raise the number to the power,
multiply the indices.
(Calculator: 43)
(4y10)3 =    y
(2x4)5 =    x
(3a2)4 = 81a8
Calculator: 34 = 81
Power of powers,
MULTIPLY the indices.
Put all those skills together....
(x4y2)2 = x   y
(2y2z4)3 =    y   z
7b0 =
Only the values the indices are attached to, become one.
2y0 =
The Zero Index:
x0
BUT...
w0 = 
(7b)0 =
5a= 5
a0 = 1
(4a)0 + 2b0 =
5x0 − 2 =
= 4 × 1 + 4 = 8
4x0 + 4
e−5 =
Negative Indices:
1
e
a−n =
a−2 =
an
1
1
a
Write as a basic fraction:
Negative Indices:
5−2 =
1
10−4 =
2−3 =
Calculator: 23 = 8
23
1
=
1
8
1
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