1.02a Indices: laws of indices for rational exponents

230 questions

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Edexcel C1 2013 January Q2
2 marks Easy -1.3
Express \(8 ^ { 2 x + 3 }\) in the form \(2 ^ { y }\), stating \(y\) in terms of \(x\).
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 C1 2005 January Q1
6 marks Easy -1.8
1
  1. Express \(11 ^ { - 2 }\) as a fraction.
  2. Evaluate \(100 ^ { \frac { 3 } { 2 } }\).
  3. Express \(\sqrt { 50 } + \frac { 6 } { \sqrt { 3 } }\) in the form \(a \sqrt { } 2 + b \sqrt { } 3\), where \(a\) and \(b\) are integers.
OCR C1 2006 January Q1
4 marks Easy -1.8
1 Solve the equations
  1. \(x ^ { \frac { 1 } { 3 } } = 2\),
  2. \(10 ^ { \prime } = 1\),
  3. \(\left( y ^ { - 2 } \right) ^ { 2 } = \frac { 1 } { 81 }\).
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 2008 January Q4
6 marks Easy -1.2
4 Solve the equations
  1. \(10 ^ { p } = 0.1\),
  2. \(\left( 25 k ^ { 2 } \right) ^ { \frac { 1 } { 2 } } = 15\),
  3. \(t ^ { - \frac { 1 } { 3 } } = \frac { 1 } { 2 }\).
OCR C1 2005 June Q5
7 marks Easy -1.3
5
  1. Simplify \(2 x ^ { \frac { 2 } { 3 } } \times 3 x ^ { - 1 }\).
  2. Express \(2 ^ { 40 } \times 4 ^ { 30 }\) in the form \(2 ^ { n }\).
  3. Express \(\frac { 26 } { 4 - \sqrt { } 3 }\) in the form \(a + b \sqrt { } 3\).
OCR C1 2008 June Q1
4 marks Easy -1.8
1 Express each of the following in the form \(4 ^ { n }\) :
  1. \(\frac { 1 } { 16 }\),
  2. 64 ,
  3. 8 .
OCR C1 2008 June Q4
5 marks Standard +0.3
4 Solve the equation \(2 x - 7 x ^ { \frac { 1 } { 2 } } + 3 = 0\).
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 Q1
3 marks Easy -1.8
1 Make \(v\) the subject of the formula \(E = \frac { 1 } { 2 } m v ^ { 2 }\).
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 2009 January Q7
4 marks Easy -1.3
7
  1. Express \(125 \sqrt { 5 }\) in the form \(5 ^ { k }\).
  2. Simplify \(\left( 4 a ^ { 3 } b ^ { 5 } \right) ^ { 2 }\).
OCR MEI C1 2007 June Q2
3 marks Easy -2.0
2 Make \(t\) the subject of the formula \(s = \frac { 1 } { 2 } a t ^ { 2 }\).
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 2015 June Q1
2 marks Easy -1.2
1 Make \(r\) the subject of the formula \(A = \pi r ^ { 2 } ( x + y )\), where \(r > 0\).
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 MEI C1 Q9
5 marks Easy -1.2
9
  1. Simplify \(\frac { 2 ^ { 6 } } { 8 ^ { 2 \frac { 1 } { 2 } } \times 2 ^ { - \frac { 1 } { 2 } } }\)
  2. Solve the equation \(x ^ { - \frac { 1 } { 3 } } = 8\).
OCR MEI C1 Q2
3 marks Moderate -0.8
2 Make \(l\) the subject of the formula \(T = 2 \pi \sqrt { \frac { l } { g } }\).
OCR MEI C1 Q4
4 marks Easy -1.3
4 Simplify the following.
  1. \(x ^ { \frac { 5 } { 2 } } \times \sqrt { x }\)
  2. \(12 x ^ { - 5 } \div 3 x ^ { - 2 }\)
OCR MEI C1 Q4
3 marks Easy -1.8
4 The surface area of the surface of a cylinder is given by the formula $$A = 2 \pi r ( r + h )$$ Rearrange this formula so that \(h\) is the subject.
OCR MEI C1 Q5
3 marks Easy -1.3
5 Solve the following equations.
  1. \(\quad 2 ^ { x } = \frac { 1 } { 8 }\).
  2. \(\quad x ^ { - \frac { 1 } { 2 } } = \frac { 1 } { 4 }\)