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43 questions at your level
Difficulty
All
Level 1
Level 2
Level 3
Level 4
Level 5
The index laws
18 questions
Lesson
Not started
Mark as done
Simplify
x
3
×
x
4
x^3 \times x^4
x
3
×
x
4
●
●●●●
Level 1
1 mark
Start
→
Mark as done
Simplify
y
8
y
2
\dfrac{y^8}{y^2}
y
2
y
8
●
●●●●
Level 1
1 mark
Start
→
Mark as done
(a)
Write
3
−
2
3^{-2}
3
−
2
as a fraction. (1 mark)
(b)
Simplify
(
x
3
)
−
2
(x^3)^{-2}
(
x
3
)
−
2
(1 mark)
●●
●●●
Level 2
2 marks
Start
→
Mark as done
(a)
Work out the value of
3
4
×
3
−
2
3^4 \times 3^{-2}
3
4
×
3
−
2
[1]
(b)
Work out the value of
27
2
3
27^{\frac{2}{3}}
2
7
3
2
[1]
(c)
Simplify
(
2
x
3
)
3
(2x^3)^3
(
2
x
3
)
3
[1]
●●
●●●
Level 2
3 marks
Start
→
Mark as done
Simplify:
(a)
x
5
×
x
3
x^5 \times x^3
x
5
×
x
3
(b)
y
9
÷
y
3
y^9 \div y^3
y
9
÷
y
3
(c)
(
z
4
)
3
(z^4)^3
(
z
4
)
3
●●●
●●
Level 3
3 marks
Start
→
Mark as done
Simplify
(
3
x
2
y
)
3
(3x^2y)^3
(
3
x
2
y
)
3
.
●●●
●●
Level 3
2 marks
Start
→
Mark as done
Simplify:
(a)
3
a
2
×
4
a
5
3a^2 \times 4a^5
3
a
2
×
4
a
5
(b)
20
b
8
÷
4
b
2
20b^8 \div 4b^2
20
b
8
÷
4
b
2
●●●
●●
Level 3
4 marks
Start
→
Mark as done
Simplify
(
2
x
3
y
2
)
4
\left(2x^3y^2\right)^4
(
2
x
3
y
2
)
4
●●●
●●
Level 3
2 marks
Start
→
Mark as done
(a)
Simplify
(
2
a
3
b
)
4
(2a^3b)^4
(
2
a
3
b
)
4
(2 marks)
(b)
Work out the value of
8
2
3
8^{\frac{2}{3}}
8
3
2
(1 mark)
●●●
●●
Level 3
3 marks
Start
→
Mark as done
Write
8
2
×
4
3
8^2 \times 4^3
8
2
×
4
3
as a single power of 2.
●●●●
●
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
.
●●●●
●
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
.
●●●●
●
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)
●●●●
●
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)
●●●●
●
Level 4
2 marks
Start
→
Mark as done
Write
4
3
×
8
4
2
10
\dfrac{4^3 \times 8^4}{2^{10}}
2
10
4
3
×
8
4
as a single power of 2.
●●●●●
Level 5
3 marks
Start
→
Mark as done
(a)
Write
9
4
×
3
5
27
3
\dfrac{9^4 \times 3^5}{27^3}
2
7
3
9
4
×
3
5
as a single power of
3
3
3
.
(b)
Hence write down the value of the expression.
●●●●●
Level 5
4 marks
Start
→
Mark as done
5
x
=
25
n
×
5
5^{x} = 25^{n} \times \sqrt{5}
5
x
=
2
5
n
×
5
5
y
=
125
n
+
1
5
5^{y} = \dfrac{125^{n+1}}{\sqrt{5}}
5
y
=
5
12
5
n
+
1
Given that
x
+
y
=
23
x + y = 23
x
+
y
=
23
work out the value of
n
n
n
.
(3 marks)
●●●●●
Level 5
3 marks
Start
→
Zero and negative indices
18 questions
Lesson
Not started
Mark as done
Write down the value of
7
0
7^0
7
0
●
●●●●
Level 1
1 mark
Start
→
Mark as done
Write down the value of
2
−
1
2^{-1}
2
−
1
●
●●●●
Level 1
1 mark
Start
→
Mark as done
5
0
+
2
3
5^0 + 2^3
5
0
+
2
3
Circle your answer.
A
8
8
8
B
9
9
9
C
10
10
10
D
11
11
11
●
●●●●
Level 1
1 mark
Start
→
Mark as done
The value of
2
−
3
2^{-3}
2
−
3
is
Circle your answer.
A
1
8
\dfrac{1}{8}
8
1
B
−
8
-8
−
8
C
−
6
-6
−
6
D
1
6
\dfrac{1}{6}
6
1
●
●●●●
Level 1
1 mark
Start
→
Mark as done
(a)
Write
3
−
2
3^{-2}
3
−
2
as a fraction. (1 mark)
(b)
Simplify
(
x
3
)
−
2
(x^3)^{-2}
(
x
3
)
−
2
(1 mark)
●●
●●●
Level 2
2 marks
Start
→
Mark as done
Write down the value of:
(a)
5
0
5^0
5
0
(b)
4
−
2
4^{-2}
4
−
2
(c)
(
1
3
)
−
1
\left(\dfrac{1}{3}\right)^{-1}
(
3
1
)
−
1
●●●
●●
Level 3
3 marks
Start
→
Mark as done
(a)
Write
2
−
5
2^{-5}
2
−
5
as a fraction.
(b)
Write
1
81
\dfrac{1}{81}
81
1
as a power of 3.
●●●
●●
Level 3
3 marks
Start
→
Mark as done
Write down the value of:
(a)
7
0
7^0
7
0
(b)
10
−
3
10^{-3}
1
0
−
3
(c)
(
1
4
)
−
2
\left(\dfrac{1}{4}\right)^{-2}
(
4
1
)
−
2
●●●
●●
Level 3
3 marks
Start
→
Mark as done
Write these three numbers in order of size, smallest first:
3
−
2
3
0
3
−
1
3^{-2} \qquad 3^0 \qquad 3^{-1}
3
−
2
3
0
3
−
1
●●●
●●
Level 3
2 marks
Start
→
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)
●●●●
●
Level 4
2 marks
Start
→
Mark as done
Solve
4
x
=
1
8
4^x = \dfrac{1}{8}
4
x
=
8
1
●●●●●
Level 5
3 marks
Start
→
Mark as done
(
x
2
−
7
x
+
11
)
x
2
−
13
x
+
42
=
1
\left(x^{2} - 7x + 11\right)^{x^{2} - 13x + 42} = 1
(
x
2
−
7
x
+
11
)
x
2
−
13
x
+
42
=
1
How many integer values of
x
x
x
satisfy this equation?
●●●●●
Level 5
4 marks
Start
→
Fractional indices
13 questions
Lesson
Not started
Mark as done
(a)
Work out the value of
3
4
×
3
−
2
3^4 \times 3^{-2}
3
4
×
3
−
2
[1]
(b)
Work out the value of
27
2
3
27^{\frac{2}{3}}
2
7
3
2
[1]
(c)
Simplify
(
2
x
3
)
3
(2x^3)^3
(
2
x
3
)
3
[1]
●●
●●●
Level 2
3 marks
Start
→
Mark as done
Evaluate:
(a)
49
1
/
2
49^{1/2}
4
9
1/2
(b)
27
1
/
3
27^{1/3}
2
7
1/3
(c)
8
2
/
3
8^{2/3}
8
2/3
●●●
●●
Level 3
4 marks
Start
→
Mark as done
Evaluate:
(a)
100
1
/
2
100^{1/2}
10
0
1/2
(b)
64
1
/
3
64^{1/3}
6
4
1/3
(c)
32
1
/
5
32^{1/5}
3
2
1/5
●●●
●●
Level 3
3 marks
Start
→
Mark as done
(a)
Simplify
(
2
a
3
b
)
4
(2a^3b)^4
(
2
a
3
b
)
4
(2 marks)
(b)
Work out the value of
8
2
3
8^{\frac{2}{3}}
8
3
2
(1 mark)
●●●
●●
Level 3
3 marks
Start
→
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
●●●●
●
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.
●●●●
●
Level 4
3 marks
Start
→
Mark as done
Write
(
16
x
8
)
3
/
4
\left(16x^8\right)^{3/4}
(
16
x
8
)
3/4
in the form
a
x
n
ax^n
a
x
n
.
●●●●●
Level 5
3 marks
Start
→
Mark as done
Solve
2
x
+
1
=
8
x
−
1
2^{x+1} = 8^{x-1}
2
x
+
1
=
8
x
−
1
.
●●●●●
Level 5
3 marks
Start
→
Mark as done
Write
(
25
x
6
)
3
/
2
\left(25x^6\right)^{3/2}
(
25
x
6
)
3/2
in the form
a
x
n
ax^n
a
x
n
.
●●●●●
Level 5
3 marks
Start
→
Mark as done
Solve
9
x
=
27
x
−
2
9^x = 27^{x-2}
9
x
=
2
7
x
−
2
●●●●●
Level 5
3 marks
Start
→
Mark as done
5
x
=
25
n
×
5
5^{x} = 25^{n} \times \sqrt{5}
5
x
=
2
5
n
×
5
5
y
=
125
n
+
1
5
5^{y} = \dfrac{125^{n+1}}{\sqrt{5}}
5
y
=
5
12
5
n
+
1
Given that
x
+
y
=
23
x + y = 23
x
+
y
=
23
work out the value of
n
n
n
.
(3 marks)
●●●●●
Level 5
3 marks
Start
→