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Use index notation and apply index laws for multiplication and division.
Number · MA4-IND-C-01
Sub-topics
Index notation
Write expressions in index form and expanded form, and evaluate powers.
Index laws
Apply index laws to multiply and divide terms with the same base, and simplify expressions using the power of a power law.
Open Math
Indices
Number · MA4-IND-C-01
Name:
Date:
Index notation
Q1
Straightforward
Write
4
×
4
×
4
4 \times 4 \times 4
4
×
4
×
4
in index form
4
n
4^n
4
n
. What is the value of
n
n
n
?
Q2
Straightforward
Write
2
×
2
×
2
×
2
×
2
2 \times 2 \times 2 \times 2 \times 2
2
×
2
×
2
×
2
×
2
in index form
2
n
2^n
2
n
. What is the value of
n
n
n
?
Q3
Straightforward
The expression
6
4
6^4
6
4
written in expanded form is
6
×
6
×
6
×
6
6 \times 6 \times 6 \times 6
6
×
6
×
6
×
6
. How many factors of
6
6
6
are there?
Q4
Straightforward
Which expression represents
7
×
7
×
7
×
7
7 \times 7 \times 7 \times 7
7
×
7
×
7
×
7
in index form?
A.
4
7
4^7
4
7
B.
7
4
7^4
7
4
C.
7
×
4
7 \times 4
7
×
4
D.
28
28
28
Q5
Moderate
Calculate
3
4
3^4
3
4
.
Q6
Moderate
Calculate
2
6
2^6
2
6
.
Q7
Moderate
Calculate
5
3
5^3
5
3
.
Q8
Moderate
Calculate
10
4
10^4
1
0
4
.
Q9
Challenging
Which has the greatest value:
2
5
2^5
2
5
,
3
3
3^3
3
3
, or
4
2
4^2
4
2
?
A.
2
5
2^5
2
5
B.
3
3
3^3
3
3
C.
4
2
4^2
4
2
D.
They are all equal.
Q10
Challenging
Evaluate
2
4
2^4
2
4
,
5
2
5^2
5
2
, and
3
3
3^3
3
3
. What is the middle value when they are ordered from smallest to largest?
Q11
Challenging
Calculate
3
4
−
2
5
3^4 - 2^5
3
4
−
2
5
.
Q12
Challenging
Which expression has the smallest value:
10
2
10^2
1
0
2
,
3
4
3^4
3
4
, or
5
3
5^3
5
3
?
A.
10
2
10^2
1
0
2
B.
3
4
3^4
3
4
C.
5
3
5^3
5
3
D.
They are all equal.
Index laws
Q13
Straightforward
Simplify
2
3
×
2
4
2^3 \times 2^4
2
3
×
2
4
. Write your answer as
2
n
2^n
2
n
— what is
n
n
n
?
Q14
Straightforward
Simplify
3
2
×
3
5
3^2 \times 3^5
3
2
×
3
5
. Write your answer as
3
n
3^n
3
n
— what is
n
n
n
?
Q15
Straightforward
Simplify
5
1
×
5
3
5^1 \times 5^3
5
1
×
5
3
. Write your answer as
5
n
5^n
5
n
— what is
n
n
n
?
Q16
Straightforward
Simplify
a
4
×
a
6
a^4 \times a^6
a
4
×
a
6
. Write your answer as
a
n
a^n
a
n
— what is
n
n
n
?
Q17
Moderate
Simplify
4
7
÷
4
3
4^7 \div 4^3
4
7
÷
4
3
. Write your answer as
4
n
4^n
4
n
— what is
n
n
n
?
Q18
Moderate
Simplify
6
5
÷
6
2
6^5 \div 6^2
6
5
÷
6
2
. Write your answer as
6
n
6^n
6
n
— what is
n
n
n
?
Q19
Moderate
Simplify
m
9
÷
m
4
m^9 \div m^4
m
9
÷
m
4
. Write your answer as
m
n
m^n
m
n
— what is
n
n
n
?
Q20
Moderate
Simplify
x
10
x
6
\dfrac{x^{10}}{x^6}
x
6
x
10
. Write your answer as
x
n
x^n
x
n
— what is
n
n
n
?
Q21
Challenging
Simplify
(
2
3
)
4
(2^3)^4
(
2
3
)
4
. Write your answer as
2
n
2^n
2
n
— what is
n
n
n
?
Q22
Challenging
Simplify
(
a
5
)
3
(a^5)^3
(
a
5
)
3
. Write your answer as
a
n
a^n
a
n
— what is
n
n
n
?
Q23
Challenging
Simplify
3
2
×
3
4
÷
3
3
3^2 \times 3^4 \div 3^3
3
2
×
3
4
÷
3
3
. Write your answer as
3
n
3^n
3
n
— what is
n
n
n
?
Q24
Challenging
Simplify
(
y
3
)
2
×
y
4
(y^3)^2 \times y^4
(
y
3
)
2
×
y
4
. Write your answer as
y
n
y^n
y
n
— what is
n
n
n
?
Worked solutions and answers at openmath.au/year-7/indices