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Law of indices
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Cards (16)
What is the definition of an
index
or power in
mathematics
?
It shows how many
times
a
number
has been
multiplied
by
itself
.
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How is the
expression
2
4
2^4
2
4
expanded
?
2
4
=
2^4 =
2
4
=
2
×
2
×
2
×
2
2 \times 2 \times 2 \times 2
2
×
2
×
2
×
2
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What is the
law of indices
for multiplication?
When multiplying
like bases
:
a
m
×
a
n
=
a^m \times a^n =
a
m
×
a
n
=
a
(
m
+
n
)
a^{(m+n)}
a
(
m
+
n
)
Example
:
c
3
×
c
2
=
c^3 \times c^2 =
c
3
×
c
2
=
c
5
c^5
c
5
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What is the
result
of
b
5
÷
b
2
b^5 \div b^2
b
5
÷
b
2
?
b
3
b^3
b
3
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How is
b
5
÷
b
3
b^5 \div b^3
b
5
÷
b
3
simplified?
b
5
÷
b
3
=
b^5 \div b^3 =
b
5
÷
b
3
=
b
5
−
3
=
b^{5-3} =
b
5
−
3
=
b
2
b^2
b
2
View source
What is the
law of indices
for
division
?
When dividing
like bases
:
a
m
÷
a
n
=
a^m \div a^n =
a
m
÷
a
n
=
a
(
m
−
n
)
a^{(m-n)}
a
(
m
−
n
)
View source
What is the result of
(
k
2
)
3
(k^2)^3
(
k
2
)
3
?
k
6
k^6
k
6
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How is
(
k
y
)
z
(k^y)^z
(
k
y
)
z
simplified?
(
k
y
)
z
=
(k^y)^z =
(
k
y
)
z
=
k
y
z
k^{yz}
k
yz
View source
What is the rule for powers to powers in
indices
?
When raising a power to another power:
(
a
m
)
n
=
(a^m)^n =
(
a
m
)
n
=
a
(
m
n
)
a^{(mn)}
a
(
mn
)
View source
What is the value of
J
0
J^0
J
0
?
1
View source
What does
J
5
÷
J
5
J^5 \div J^5
J
5
÷
J
5
equal?
1
View source
What is the summary of the
laws of indices
?
Multiplication
:
a
m
×
a
n
=
a^m \times a^n =
a
m
×
a
n
=
a
(
m
+
n
)
a^{(m+n)}
a
(
m
+
n
)
Division
:
a
m
÷
a
n
=
a^m \div a^n =
a
m
÷
a
n
=
a
(
m
−
n
)
a^{(m-n)}
a
(
m
−
n
)
Power to Power
:
(
a
m
)
n
=
(a^m)^n =
(
a
m
)
n
=
a
(
m
n
)
a^{(mn)}
a
(
mn
)
Power of Zero
:
a
0
=
a^0 =
a
0
=
1
1
1
View source
How is a
negative index
expressed in terms of a
fraction
?
d
−
n
=
d^{-n} =
d
−
n
=
1
d
n
\frac{1}{d^n}
d
n
1
View source
What is the
result
of
d
4
÷
d
5
d^4 \div d^5
d
4
÷
d
5
?
d
−
1
d^{-1}
d
−
1
View source
What happens when there are
negative
indices
?
Negative indices become
fractions
:
d
−
n
=
d^{-n} =
d
−
n
=
1
d
n
\frac{1}{d^n}
d
n
1
View source
What is the general rule for
decimals
in
indices
?
Decimals can be expressed as sums or products in indices.
View source
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