Evaluate numerical powers

A question is this type if and only if it asks to evaluate a specific numerical expression involving powers or roots with no algebraic variables, such as 16^(1/2), 81^(3/4), or (1/25)^(-1/2).

45 questions · Easy -1.6

1.02a Indices: laws of indices for rational exponents
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Edexcel C1 2005 January Q1
3 marks Easy -1.8
  1. Write down the value of \(16 ^ { \frac { 1 } { 2 } }\).
  2. Find the value of \(16 ^ { - \frac { 3 } { 2 } }\).
Edexcel C1 2009 January Q1
3 marks Easy -1.8
  1. Write down the value of \(125 ^ { \frac { 1 } { 3 } }\).
  2. Find the value of \(125 ^ { - \frac { 2 } { 3 } }\).
Edexcel C1 2005 June Q1
3 marks Easy -1.8
  1. Write down the value of \(8 ^ { \frac { 1 } { 3 } }\).
  2. Find the value of \(8 ^ { - \frac { 2 } { 3 } }\).
Edexcel C1 2011 June Q1
3 marks Easy -1.5
Find the value of
  1. \(25 ^ { \frac { 1 } { 2 } }\)
  2. \(25 ^ { - \frac { 3 } { 2 } }\)
Edexcel C1 Q3
4 marks Easy -1.8
Find the value of
  1. \(81 ^ { \frac { 1 } { 2 } }\),
  2. \(81 ^ { \frac { 3 } { 4 } }\),
  3. \(81 ^ { - \frac { 3 } { 4 } }\).
OCR C1 2007 January Q2
4 marks Easy -1.8
2 Evaluate
  1. \(6 ^ { 0 }\),
  2. \(2 ^ { - 1 } \times 32 ^ { \frac { 4 } { 5 } }\).
OCR C1 Specimen Q1
4 marks Easy -1.8
1 Write down the exact values of
  1. \(4 ^ { - 2 }\),
  2. \(( 2 \sqrt { } 2 ) ^ { 2 }\),
  3. \(\left( 1 ^ { 3 } + 2 ^ { 3 } + 3 ^ { 3 } \right) ^ { \frac { 1 } { 2 } }\).
OCR MEI C1 2008 January Q3
4 marks Easy -1.8
3
  1. Write down the value of \(\left( \frac { 1 } { 4 } \right) ^ { 0 }\).
  2. Find the value of \(16 ^ { - \frac { 3 } { 2 } }\).
OCR MEI C1 2009 January Q1
2 marks Easy -1.8
1 State the value of each of the following.
  1. \(2 ^ { - 3 }\)
  2. \(9 ^ { 0 }\)
OCR MEI C1 2015 June Q3
4 marks Easy -1.8
3 Evaluate the following.
  1. \(200 ^ { \circ }\)
  2. \(\left( \frac { 25 } { 9 } \right) ^ { - \frac { 1 } { 2 } }\)
OCR C1 2012 January Q4
5 marks Easy -1.8
4 Evaluate
  1. \(3 ^ { - 2 }\),
  2. \(16 ^ { \frac { 3 } { 4 } }\),
  3. \(\frac { \sqrt { 200 } } { \sqrt { 8 } }\).
OCR MEI C1 2007 January Q6
4 marks Easy -1.5
6 Find the value of each of the following, giving each answer as an integer or fraction as appropriate.
  1. \(25 ^ { \frac { 3 } { 2 } }\)
  2. \(\left( \frac { 7 } { 3 } \right) ^ { - 2 }\)
OCR MEI C1 2011 January Q2
4 marks Easy -1.8
2
  1. Write down the value of each of the following.
    (A) \(4 ^ { - 2 }\) (B) \(9 ^ { 0 }\)
  2. Find the value of \(\left( \frac { 64 } { 125 } \right) ^ { \frac { 4 } { 3 } }\).
OCR MEI C1 2013 January Q1
4 marks Easy -1.8
1 Find the value of each of the following.
  1. \(\left( \frac { 5 } { 3 } \right) ^ { - 2 }\)
  2. \(81 ^ { \frac { 3 } { 4 } }\)
OCR MEI C1 2016 June Q1
5 marks Easy -1.8
1 Find the value of each of the following.
  1. \(3 ^ { 0 }\)
  2. \(9 ^ { \frac { 3 } { 2 } }\)
  3. \(\left( \frac { 4 } { 5 } \right) ^ { - 2 }\)
OCR MEI C4 Q2
Standard +0.8
2 A civilisation which works in base 5 sends out the first 6 digits of \(\pi\) as 3.032 32. Convert this to base 10.
OCR MEI Paper 2 2023 June Q3
3 marks Moderate -0.8
3 In this question you must show detailed reasoning.
Find the smallest possible positive integers \(m\) and \(n\) such that \(\left( \frac { 64 } { 49 } \right) ^ { - \frac { 3 } { 2 } } = \frac { m } { n }\).
Edexcel C1 Q1
Easy -1.3
  1. (a) Write down the value of \(8 ^ { \frac { 1 } { 3 } }\).
    (b) Find the value of \(8 ^ { - \frac { 2 } { 3 } }\).
  2. Given that \(y = 6 x - \frac { 4 } { x ^ { 2 } } , x \neq 0\),
    (a) find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\),
    (b) find \(\int y \mathrm {~d} x\).
Edexcel C1 Q1
3 marks Easy -1.8
  1. Write down the value of \(16^{-1}\). [1]
  2. Find the value of \(16^{-\frac{1}{2}}\). [2]
Edexcel C1 Q1
3 marks Easy -1.8
  1. Write down the value of \(8^{-1}\). [1]
  2. Find the value of \(8^{-\frac{2}{3}}\). [2]
Edexcel C1 Q2
4 marks Easy -1.8
  1. Find the value of \(8^{-1}\). [2]
  2. Simplify \(\frac{15x^4}{3x}\). [2]
OCR MEI C1 Q5
4 marks Easy -1.8
Find the value of the following.
  1. \(\left(\frac{1}{3}\right)^{-2}\) [2]
  2. \(16^{\frac{1}{4}}\) [2]
OCR MEI C1 2006 June Q9
5 marks Easy -1.3
Simplify the following.
  1. \(\frac{16^{\frac{1}{4}}}{81^{\frac{1}{4}}}\) [2]
  2. \(\frac{12(a^3b^2c)^4}{4a^2c^6}\) [3]
OCR MEI C1 2009 June Q7
3 marks Easy -1.8
Find the value of each of the following.
  1. \(5^2 \times 5^{-2}\) [2]
  2. \(100^{\frac{1}{2}}\) [1]
OCR MEI C1 2010 June Q2
5 marks Easy -1.8
  1. Simplify \((5a^2b)^3 \times 2b^4\). [2]
  2. Evaluate \(\left(\frac{1}{16}\right)^{-1}\). [1]
  3. Evaluate \((16)^{\frac{1}{2}}\). [2]