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43 questions at your level
Difficulty
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Level 1
Level 2
Level 3
Level 4
Level 5
The index laws
18 questions
Lesson
Not started
Mark as done
Write
8
2
×
4
3
8^2 \times 4^3
8
2
×
4
3
as a single power of 2.
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●
Level 4
3 marks
Start
→
Mark as done
3
n
×
9
2
=
3
11
3^n \times 9^2 = 3^{11}
3
n
×
9
2
=
3
11
. Work out the value of
n
n
n
.
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●
Level 4
3 marks
Start
→
Mark as done
Write
27
2
×
9
2
27^2 \times 9^2
2
7
2
×
9
2
as a single power of
3
3
3
.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
(
2
n
)
3
÷
2
5
=
2
16
\left(2^n\right)^3 \div 2^5 = 2^{16}
(
2
n
)
3
÷
2
5
=
2
16
Work out the value of
n
n
n
.
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●
Level 4
3 marks
Start
→
Mark as done
Write
(
2
x
3
y
)
4
×
3
x
y
5
6
x
7
y
11
\dfrac{(2x^{3}y)^{4} \times 3xy^{5}}{6x^{7}y^{11}}
6
x
7
y
11
(
2
x
3
y
)
4
×
3
x
y
5
in the form
a
x
b
y
c
ax^{b}y^{c}
a
x
b
y
c
where
a
a
a
,
b
b
b
and
c
c
c
are integers.
(3 marks)
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●
Level 4
3 marks
Start
→
Mark as done
5
x
−
2
(
2
x
2
−
3
x
7
)
=
a
+
b
x
n
5x^{-2}(2x^{2} - 3x^{7}) = a + bx^{n}
5
x
−
2
(
2
x
2
−
3
x
7
)
=
a
+
b
x
n
for all the values of
x
x
x
that are not zero.
Find the value of
a
a
a
, the value of
b
b
b
and the value of
n
n
n
.
(2 marks)
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●
Level 4
2 marks
Start
→
Zero and negative indices
18 questions
Lesson
Not started
Mark as done
Evaluate
(
2
5
)
−
3
\left(\dfrac{2}{5}\right)^{-3}
(
5
2
)
−
3
. Give your answer as a fraction.
●●●●
●
Level 4
2 marks
Start
→
Mark as done
Write
6
x
2
2
x
−
3
\dfrac{6x^2}{2x^{-3}}
2
x
−
3
6
x
2
in the form
a
x
n
ax^n
a
x
n
.
●●●●
●
Level 4
2 marks
Start
→
Mark as done
5
2
x
×
5
−
3
=
5
7
5^{2x} \times 5^{-3} = 5^{7}
5
2
x
×
5
−
3
=
5
7
. Work out the value of
x
x
x
.
●●●●
●
Level 4
2 marks
Start
→
Mark as done
Evaluate
(
3
4
)
−
2
\left(\dfrac{3}{4}\right)^{-2}
(
4
3
)
−
2
. Give your answer as a fraction.
●●●●
●
Level 4
2 marks
Start
→
Mark as done
Write
12
x
−
4
3
x
2
\dfrac{12x^{-4}}{3x^2}
3
x
2
12
x
−
4
in the form
a
x
n
ax^n
a
x
n
.
●●●●
●
Level 4
2 marks
Start
→
Mark as done
Write
(
2
x
3
y
)
4
×
3
x
y
5
6
x
7
y
11
\dfrac{(2x^{3}y)^{4} \times 3xy^{5}}{6x^{7}y^{11}}
6
x
7
y
11
(
2
x
3
y
)
4
×
3
x
y
5
in the form
a
x
b
y
c
ax^{b}y^{c}
a
x
b
y
c
where
a
a
a
,
b
b
b
and
c
c
c
are integers.
(3 marks)
●●●●
●
Level 4
3 marks
Start
→
Mark as done
5
x
−
2
(
2
x
2
−
3
x
7
)
=
a
+
b
x
n
5x^{-2}(2x^{2} - 3x^{7}) = a + bx^{n}
5
x
−
2
(
2
x
2
−
3
x
7
)
=
a
+
b
x
n
for all the values of
x
x
x
that are not zero.
Find the value of
a
a
a
, the value of
b
b
b
and the value of
n
n
n
.
(2 marks)
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●
Level 4
2 marks
Start
→
Fractional indices
13 questions
Lesson
Not started
Mark as done
Evaluate
16
−
3
/
4
16^{-3/4}
1
6
−
3/4
. Give your answer as a fraction.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
Evaluate
(
25
9
)
−
1
/
2
\left(\dfrac{25}{9}\right)^{-1/2}
(
9
25
)
−
1/2
. Give your answer as a fraction.
●●●●
●
Level 4
2 marks
Start
→
Mark as done
Evaluate:
(a)
27
2
/
3
27^{2/3}
2
7
2/3
(b)
81
3
/
4
81^{3/4}
8
1
3/4
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●
Level 4
4 marks
Start
→
Mark as done
Evaluate
(
8
125
)
−
2
/
3
\left(\dfrac{8}{125}\right)^{-2/3}
(
125
8
)
−
2/3
. Give your answer as a fraction.
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●
Level 4
3 marks
Start
→