Simplify algebraic expressions with indices

A question is this type if and only if it asks to simplify an algebraic expression involving powers, roots, or fractional indices, such as (25x^4)^(1/2) or (2x^(-1/4))^4, typically resulting in the form kx^n.

42 questions · Easy -1.3

1.02a Indices: laws of indices for rational exponents
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Edexcel P1 2023 October Q2
4 marks Easy -1.2
  1. Given that
$$a = \frac { 1 } { 64 } x ^ { 2 } \quad b = \frac { 16 } { \sqrt { x } }$$ express each of the following in the form \(k x ^ { n }\) where \(k\) and \(n\) are simplified constants.
  1. \(a ^ { \frac { 1 } { 2 } }\)
  2. \(\frac { 16 } { b ^ { 3 } }\)
  3. \(\left( \frac { a b } { 2 } \right) ^ { - \frac { 4 } { 3 } }\)
Edexcel C12 2018 January Q3
4 marks Easy -1.3
3. Simplify fully
  1. \(\left( 3 x ^ { \frac { 1 } { 2 } } \right) ^ { 4 }\)
  2. \(\frac { 2 y ^ { 7 } \times ( 4 y ) ^ { - 2 } } { 3 y }\)
Edexcel C12 2015 June Q3
3 marks Easy -1.2
3. Given that $$y = \frac { 1 } { 27 } x ^ { 3 }$$ express each of the following in the form \(k x ^ { n }\) where \(k\) and \(n\) are constants.
  1. \(y ^ { \frac { 1 } { 3 } }\)
  2. \(3 y ^ { - 1 }\)
  3. \(\sqrt { ( 27 y ) }\)
Edexcel C12 2017 June Q2
4 marks Easy -1.3
  1. Simplify the following expressions fully.
    1. \(\left( \frac { 1 } { 9 } x ^ { 4 } \right) ^ { 0.5 }\)
    2. \(\left( \frac { x } { \sqrt { 2 } } \right) ^ { - 2 }\)
    3. \(x \sqrt { 3 } \div \sqrt { \frac { 48 } { x ^ { 4 } } }\)
Edexcel C12 2018 June Q4
5 marks Easy -1.2
4. Given that $$y = \frac { 64 x ^ { 6 } } { 25 } , x > 0$$ express each of the following in the form \(k x ^ { n }\) where \(k\) and \(n\) are constants.
  1. \(y ^ { - \frac { 1 } { 2 } }\)
  2. \(( 25 y ) ^ { \frac { 2 } { 3 } }\)
Edexcel C12 Specimen Q1
3 marks Easy -1.5
Simplify fully
  1. \(\left( 25 x ^ { 4 } \right) ^ { \frac { 1 } { 2 } }\),
  2. \(\left( 25 x ^ { 4 } \right) ^ { - \frac { 3 } { 2 } }\).
Edexcel C1 2011 January Q1
4 marks Easy -1.3
  1. Find the value of \(16 ^ { - \frac { 1 } { 4 } }\)
  2. Simplify \(x \left( 2 x ^ { - \frac { 1 } { 4 } } \right) ^ { 4 }\)
Edexcel C1 2013 January Q1
3 marks Easy -1.2
Factorise completely \(x - 4 x ^ { 3 }\)
Edexcel C1 2012 June Q2
4 marks Easy -1.3
2. (a) Evaluate \(( 32 ) ^ { \frac { 3 } { 5 } }\), giving your answer as an integer.
(b) Simplify fully \(\left( \frac { 25 x ^ { 4 } } { 4 } \right) ^ { - \frac { 1 } { 2 } }\)
Edexcel C1 2013 June Q3
5 marks Easy -1.3
3. (a) Find the value of \(8 ^ { \frac { 5 } { 3 } }\) (b) Simplify fully \(\frac { \left( 2 x ^ { \frac { 1 } { 2 } } \right) ^ { 3 } } { 4 x ^ { 2 } }\)
Edexcel C1 2008 January Q2
3 marks Easy -1.3
  1. Write down the value of \(16 ^ { \frac { 1 } { 4 } }\).
  2. Simplify \(\left( 16 x ^ { 12 } \right) ^ { \frac { 3 } { 4 } }\).
Edexcel C1 2007 June Q2
4 marks Easy -1.3
  1. Find the value of \(8 ^ { \frac { 4 } { 3 } }\).
  2. Simplify \(\frac { 15 x ^ { \frac { 4 } { 3 } } } { 3 x }\).
Edexcel C1 2014 June Q2
4 marks Easy -1.3
  1. Evaluate \(81 ^ { \frac { 3 } { 2 } }\)
  2. Simplify fully \(x ^ { 2 } \left( 4 x ^ { - \frac { 1 } { 2 } } \right) ^ { 2 }\) \includegraphics[max width=\textwidth, alt={}, center]{6db8acbd-7f61-46ff-8fdc-f0f4a8363aa6-03_83_150_2675_1804}
OCR MEI C1 2007 June Q5
4 marks Easy -1.3
5
  1. Find \(a\), given that \(a ^ { 3 } = 64 x ^ { 12 } y ^ { 3 }\).
  2. Find the value of \(\left( \frac { 1 } { 2 } \right) ^ { - 5 }\).
OCR MEI C1 2008 June Q6
5 marks Easy -1.3
6
  1. Find the value of \(\left( \frac { 1 } { 25 } \right) ^ { - \frac { 1 } { 2 } }\).
  2. Simplify \(\frac { \left( 2 x ^ { 2 } y ^ { 3 } z \right) ^ { 5 } } { 4 y ^ { 2 } z }\).
OCR MEI C1 Q4
4 marks Easy -1.3
4 Simplify the following.
  1. \(x ^ { \frac { 5 } { 2 } } \times \sqrt { x }\)
  2. \(12 x ^ { - 5 } \div 3 x ^ { - 2 }\)
Edexcel C1 2014 June Q2
4 marks Easy -1.3
2.(a)Write down the value of \(32 ^ { \frac { 1 } { 5 } }\) (b)Simplify fully \(\left( 32 x ^ { 5 } \right) ^ { - \frac { 2 } { 5 } }\) I敖
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OCR C1 2009 January Q2
4 marks Easy -1.3
2 Simplify
  1. \(( \sqrt [ 3 ] { x } ) ^ { 6 }\),
  2. \(\frac { 3 y ^ { 4 } \times ( 10 y ) ^ { 3 } } { 2 y ^ { 5 } }\).
OCR C1 2011 June Q3
5 marks Easy -1.3
3 Simplify
  1. \(\frac { ( 4 x ) ^ { 2 } \times 2 x ^ { 3 } } { x }\),
  2. \(\left( 36 x ^ { - 2 } \right) ^ { - \frac { 1 } { 2 } }\).
OCR MEI C1 2012 January Q2
5 marks Easy -1.3
2
  1. Evaluate \(9 ^ { - \frac { 1 } { 2 } }\).
  2. Simplify \(\frac { \left( 4 x ^ { 4 } \right) ^ { 3 } y ^ { 2 } } { 2 x ^ { 2 } y ^ { 5 } }\).
OCR MEI C1 2013 January Q2
3 marks Easy -1.2
2 Simplify \(\frac { \left( 4 x ^ { 5 } y \right) ^ { 3 } } { \left( 2 x y ^ { 2 } \right) \times \left( 8 x ^ { 10 } y ^ { 4 } \right) }\).
OCR MEI C1 2014 June Q1
5 marks Easy -1.3
1
  1. Evaluate \(\left( \frac { 1 } { 27 } \right) ^ { \frac { 2 } { 3 } }\).
  2. Simplify \(\frac { \left( 4 a ^ { 2 } c \right) ^ { 3 } } { 32 a ^ { 4 } c ^ { 7 } }\).
OCR H240/01 2020 November Q2
8 marks Easy -1.3
2 Simplify fully.
  1. \(\sqrt { 12 a } \times \sqrt { 3 a ^ { 5 } }\)
  2. \(\left( 64 b ^ { 3 } \right) ^ { \frac { 1 } { 3 } } \times \left( 4 b ^ { 4 } \right) ^ { - \frac { 1 } { 2 } }\)
  3. \(7 \times 9 ^ { 3 c } - 4 \times 27 ^ { 2 c }\)
OCR H240/02 Q1
4 marks Easy -1.3
1 Simplify fully.
  1. \(\sqrt { a ^ { 3 } } \times \sqrt { 16 a }\)
  2. \(\quad \left( 4 b ^ { 6 } \right) ^ { \frac { 5 } { 2 } }\)
OCR MEI AS Paper 1 Specimen Q1
2 marks Easy -1.2
1 Simplify \(\frac { \left( 2 x ^ { 2 } y \right) ^ { 3 } \times 4 x ^ { 3 } y ^ { 5 } } { 2 x y ^ { 10 } }\).