GCSEMathsEdexcelHigherExam Questions2. AlgebraAlgebraic Roots & Indices

Algebraic Roots & Indices (Edexcel GCSE Maths: Higher): Exam Questions

Exam code: 1MA1

2 hours51 questions
Easy
Medium
Hard
11 mark

Simplify      open parentheses m to the power of negative 2 end exponent close parentheses to the power of 5

How did you do?

2a1 mark

Simplify   m to the power of 5 space divided by space m cubed

How did you do?

2b2 marks

Simplify    5 x to the power of 4 y cubed space cross times space x squared y

How did you do?

3a1 mark

Simplify    m to the power of 5 space cross times space m cubed

How did you do?

3b1 mark

Simplify      p to the power of 6 over p squared

How did you do?

4a1 mark

Simplify      p squared space cross times space p to the power of 5

How did you do?

4b1 mark

Simplify      g to the power of 6 space divided by space g to the power of 4

How did you do?

4c1 mark

Simplify       open parentheses k cubed close parentheses squared

How did you do?

51 mark

Simplify    t to the power of 8 space divided by space t cubed

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6a1 mark

Simplify      open parentheses t cubed close parentheses squared

How did you do?

6b1 mark

Simplify     w to the power of 9 over w to the power of 4

How did you do?

71 mark

Simplify  left parenthesis 3 x squared space y right parenthesis to the power of 0

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81 mark

Simplify  x to the power of 9 over x squared

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91 mark

Write down the value of g to the power of 0

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101 mark

Simplify  e to the power of 8 divided by e squared

How did you do?

111 mark

Simplify w to the power of 1 space cross times space w to the power of 0

  • 1

  • 0

  • w

  • w squared

Choose your answer

121 mark

Given that y to the power of 18 space divided by space y to the power of 6 space equals space y to the power of k , find the value of k.

k = ...................

How did you do?

131 mark

Simplify a to the power of 6 space divided by space a squared

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141 mark

Simplify open parentheses b to the power of 5 close parentheses cubed

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151 mark

Simplify fraction numerator 3 y cubed over denominator y to the power of negative 4 end exponent end fraction

How did you do?

12 marks

Simplify     5 u squared w to the power of 4 space cross times space 7 u w cubed

How did you do?

2
Sme Calculator2 marks

Simplify     open parentheses 9 x to the power of 8 y cubed close parentheses to the power of 1 half end exponent

How did you do?

3a1 mark

Simplify       a to the power of 4 space cross times space a to the power of 5

How did you do?

3b2 marks

Simplify           fraction numerator 45 e to the power of 6 f to the power of 8 over denominator 5 e f squared end fraction

How did you do?

3c
Sme Calculator1 mark

Write down the value of   9 to the power of 1 half end exponent

How did you do?

4a1 mark

Simplify        x to the power of 7 space cross times space x cubed

How did you do?

4b1 mark

Simplify       open parentheses m to the power of 4 close parentheses cubed

How did you do?

4c2 marks

Simplify    fraction numerator 36 a f to the power of 8 over denominator 12 a to the power of 5 f squared end fraction

How did you do?

52 marks

Simplify      open parentheses 3 x squared y to the power of 4 close parentheses cubed

How did you do?

6a1 mark

Simplify      open parentheses p cubed close parentheses squared

How did you do?

6b1 mark

Simplify     t to the power of 8 over t cubed

How did you do?

6c1 mark

2 cubed space cross times space 2 to the power of n space equals space 2 to the power of 9

Work out the value of n.

How did you do?

6d
Sme Calculator1 mark

2 x cubed space equals space 128

Work out the value of x.

How did you do?

72 marks

Simplify fully    fraction numerator p cubed space cross times space p to the power of 4 over denominator p squared end fraction

How did you do?

8a
Sme Calculator2 marks

Solve     3 x squared space equals space 147

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8b
Sme Calculator1 mark

Work out the value of 2 to the power of negative 3 end exponent

How did you do?

8c
Sme Calculator2 marks

Simplify    open parentheses 3 x squared close parentheses cubed

How did you do?

8d2 marks

w space equals space 4 p space minus space 16

Make p spacethe subject of this formula.

How did you do?

92 marks

Simplify       2 a cubed b space cross times space 5 a squared b cubed

How did you do?

102 marks

Simplify fully    fraction numerator n to the power of 7 space cross times space n cubed over denominator n to the power of 6 end fraction

How did you do?

11a1 mark

Simplify    m cubed space cross times space m to the power of 4

How did you do?

11b2 marks

Simplify     open parentheses 5 n p cubed close parentheses cubed

How did you do?

11c2 marks

Simplify       fraction numerator 32 q to the power of 9 r to the power of 4 over denominator 4 q cubed r end fraction

How did you do?

12
Sme Calculator2 marks

Simplify  left parenthesis 2 x cubed y to the power of 5 space right parenthesis to the power of 4

How did you do?

13
Sme Calculator2 marks

Simplify   left parenthesis 16 e to the power of 10 space f to the power of 6 space right parenthesis to the power of 1 half end exponent

How did you do?

143 marks

Simplify fully.

fraction numerator 3 a to the power of 8 cross times 2 a to the power of 5 over denominator a squared end fraction

How did you do?

152 marks

Show that a to the power of 5 cross times space open parentheses a cubed close parentheses squared can be expressed as a to the power of 11.

How did you do?

162 marks

Simplify fraction numerator 3 b squared c over denominator d squared end fraction cross times fraction numerator 10 b c to the power of 5 d over denominator c end fraction

How did you do?

172 marks

Simplify fully open parentheses x to the power of 6 over 125 close parentheses to the power of 2 over 3 end exponent

How did you do?

1
Sme Calculator3 marks

16 to the power of 1 fifth end exponent space cross times space 2 to the power of x space equals space 8 to the power of 3 over 4 end exponent

Work out the exact value of x.

How did you do?

2a1 mark

p cubed space cross times space p to the power of x space equals space p to the power of 9

Find the value of x.

How did you do?

2b1 mark

open parentheses 7 squared close parentheses to the power of y space equals space 7 to the power of 10

Find the value of y.

How did you do?

2c2 marks

100 to the power of a space cross times space 1000 to the power of b can be written in the form 10 to the power of w

Show that w space equals space 2 a space plus space 3 b

How did you do?

3a
Sme Calculator1 mark

Simplify fully    open parentheses 3 e close parentheses to the power of 0

How did you do?

3b
Sme Calculator2 marks

Simplify fully      open parentheses fraction numerator 64 x to the power of 6 over denominator 25 y squared end fraction close parentheses to the power of negative 1 half end exponent

How did you do?

41 mark

Given that  open parentheses cube root of 1 over x end root close parentheses to the power of 4 equals x to the power of m

find the value of m

m = .................................................

How did you do?

5
Sme Calculator2 marks

Given that  fraction numerator 7 to the power of 206 cross times 7 to the power of m over denominator 7 to the power of 214 end fraction equals 7 to the power of negative 3 end exponent

find the value of m

m = ..............................................

How did you do?

6
Sme Calculator3 marks

Simplify completely      open parentheses fraction numerator 16 w to the power of 8 over denominator y to the power of 20 end fraction close parentheses to the power of begin inline style negative 3 over 4 end style end exponent

How did you do?

7
Sme Calculator4 marks

Given that  n to the power of open parentheses negative 4 over 5 close parentheses end exponent equals open parentheses 1 half close parentheses to the power of 4 where n greater than 0

find the value of n.

n space= .............................................

How did you do?

82 marks

Given that  fraction numerator y to the power of 5 space cross times space y to the power of n over denominator y to the power of 6 end fraction equals y to the power of 13

work out the value of n.

n space equals space...........................................

How did you do?

9
Sme Calculator1 mark

Simplify fully  open parentheses fraction numerator 9 t to the power of 4 w to the power of 9 over denominator 18 t to the power of 6 w to the power of 10 end fraction close parentheses to the power of negative 2 end exponent

How did you do?

104 marks

Given that  4 to the power of k plus 3 space end exponent equals space 16 cross times 2 to the power of k

find the value of k.
Show your working clearly.

k space equals .................................................

How did you do?

11
Sme Calculator3 marks

Write 27 cross times open parentheses 3 squared close parentheses to the power of 7 as a single power of 3

How did you do?

12
Sme Calculator3 marks

Write 16 space cross times space 8 to the power of 2 x end exponent as a power of 2 in terms of x

How did you do?

131 mark

Choose the expression that is equivalent to 4 left parenthesis 2 to the power of n space plus space 2 to the power of n minus 1 end exponent right parenthesis

  • 2 to the power of n plus 2 end exponent space plus space 2 to the power of n plus 1 end exponent

  • 2 to the power of 2 n end exponent space plus space 2 to the power of 2 open parentheses n minus 1 close parentheses end exponent

  • 8 to the power of n space plus space 8 to the power of n minus 1 end exponent

  • 2 to the power of n plus 2 end exponent space plus space 2 to the power of n minus 1 end exponent

Choose your answer

143 marks

Simplify fully   fraction numerator a cubed b squared over denominator c d end fraction cross times fraction numerator c over denominator a b to the power of 5 end fraction

How did you do?

15
Sme Calculator4 marks

square root of 6 squared plus 8 squared end root space equals space cube root of 125 a cubed end root

Work out the value of a.

How did you do?

16
Sme Calculator2 marks

open parentheses a r to the power of b close parentheses to the power of 4 equals 16 r to the power of 20  where a and b are positive integers.

Work out a and b

a equals...................... b equals......................

How did you do?

17a2 marks

Simplify 4 a to the power of 1 half end exponent cross times 3 a squared

How did you do?

17b3 marks

Simplify open square brackets fraction numerator 2 a squared over denominator a to the power of negative 3 end exponent end fraction close square brackets cubed

How did you do?

183 marks

Show that cube root of a to the power of 4 space end root cross times 1 over a  can be expressed as a to the power of 1 third end exponent.

How did you do?

193 marks

Show that  open parentheses a cubed close parentheses to the power of negative 1 third end exponent cross times open parentheses a squared close parentheses to the power of 1 half end exponent equals 1.

How did you do?