igureMaths
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Level 5
The index laws
18 questions
Lesson
Not started
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.
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Level 5
3 marks
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→
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
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
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
→