Express in terms of substitution

A question is this type if and only if it provides a substitution like y = 2^x or m = 2^n and asks to express other exponential expressions in terms of the new variable.

4 questions · Easy -1.1

1.02a Indices: laws of indices for rational exponents
Sort by: Default | Easiest first | Hardest first
Edexcel P1 2019 January Q2
3 marks Moderate -0.8
  1. Given
$$\frac { 3 ^ { x } } { 3 ^ { 4 y } } = 27 \sqrt { 3 }$$ find \(y\) as a simplified function of \(x\).
Edexcel P1 2020 January Q2
5 marks Easy -1.2
2. Given \(y = 3 ^ { x }\), express each of the following in terms of \(y\). Write each expression in its simplest form.
  1. \(3 ^ { 3 x }\)
  2. \(\frac { 1 } { 3 ^ { x - 2 } }\)
  3. \(\frac { 81 } { 9 ^ { 2 - 3 x } }\)
Edexcel P1 2024 June Q2
6 marks Easy -1.2
    1. Given that \(m = 2 ^ { n }\), express each of the following in simplest form in terms of \(m\).
      1. \(2 ^ { n + 3 }\)
    2. \(16 ^ { 3 n }\) (ii) In this question you must show all stages of your working.
    Solutions relying on calculator technology are not acceptable. Solve the equation $$x \sqrt { 3 } - 3 = x + \sqrt { 3 }$$ giving your answer in the form \(p + q \sqrt { 3 }\) where \(p\) and \(q\) are integers.
Edexcel C12 2019 January Q2
4 marks Easy -1.2
2. Given \(y = 2 ^ { x }\), express each of the following in terms of \(y\). Write each expression in its simplest form.
  1. \(2 ^ { 2 x }\)
  2. \(2 ^ { x + 3 }\)
  3. \(\frac { 1 } { 4 ^ { 2 x - 3 } }\)