Rewrite with fractional indices

A question is this type if and only if it asks to rewrite an expression involving roots and powers in the form Ax^p + Bx^q, such as converting (5x^2 + √(x^3))/∛(8x) to this form.

4 questions · Easy -1.1

1.02a Indices: laws of indices for rational exponents
Sort by: Default | Easiest first | Hardest first
Edexcel P1 2023 June Q4
7 marks Moderate -0.8
  1. In this question you must show all stages of your working.
    1. Write
    $$y = \frac { 5 x ^ { 2 } + \sqrt { x ^ { 3 } } } { \sqrt [ 3 ] { 8 x } }$$ in the form $$y = A x ^ { p } + B x ^ { q }$$ where \(A , B , p\) and \(q\) are constants to be found.
  2. Hence find \(\frac { \mathrm { d } y } { \mathrm {~d} x }\) giving each coefficient in simplest form.
Edexcel C1 2011 June Q6
7 marks Easy -1.2
6. Given that \(\frac { 6 x + 3 x ^ { \frac { 5 } { 2 } } } { \sqrt { } x }\) can be written in the form \(6 x ^ { p } + 3 x ^ { q }\),
  1. write down the value of \(p\) and the value of \(q\). Given that \(\frac { \mathrm { d } y } { \mathrm {~d} x } = \frac { 6 x + 3 x ^ { \frac { 5 } { 2 } } } { \sqrt { } x }\), and that \(y = 90\) when \(x = 4\),
  2. find \(y\) in terms of \(x\), simplifying the coefficient of each term.
AQA C2 2012 January Q3
3 marks Easy -1.2
3
  1. Write \(\sqrt [ 4 ] { x ^ { 3 } }\) in the form \(x ^ { k }\).
  2. Write \(\frac { 1 - x ^ { 2 } } { \sqrt [ 4 ] { x ^ { 3 } } }\) in the form \(x ^ { p } - x ^ { q }\).
AQA Paper 3 2023 June Q4
5 marks Easy -1.2
Express $$5 - \frac{\sqrt[3]{x}}{x^2}$$ in the form $$5x^p - x^q$$ where \(p\) and \(q\) are constants. [2 marks]