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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OCR MEI Paper 1 2020 November Q1
2 marks Easy -1.3
1 Simplify \(\left( \frac { 27 } { x ^ { 9 } } \right) ^ { \frac { 2 } { 3 } } \times \left( \frac { x ^ { 4 } } { 9 } \right)\).
[0pt] [2]
AQA AS Paper 2 2021 June Q1
1 marks Easy -1.8
1 Express as a single power of \(a\) $$\frac { a ^ { 2 } } { \sqrt { a } }$$ where \(a \neq 0\) Circle your answer. \(a ^ { 1 }\) \(a ^ { \frac { 3 } { 2 } }\) \(a ^ { \frac { 5 } { 2 } }\) \(a ^ { 4 }\)
Edexcel P1 2018 Specimen Q2
5 marks Easy -1.2
  1. Given that \(3^{-1.5} = a\sqrt{3}\) find the exact value of \(a\) [2]
  2. Simplify fully \(\frac{(2x^{\frac{1}{2}})^3}{4x^2}\) [3]
OCR MEI C1 2013 June Q3
5 marks Easy -1.8
  1. Evaluate \((0.2)^{-2}\). [2]
  2. Simplify \((16a^{12})^{\frac{1}{4}}\). [3]
OCR MEI C1 Q7
3 marks Easy -1.2
Simplify \(\frac{(4x^5 y)^3}{(2xy^2) \times (8x^{10}y^4)}\). [3]
OCR MEI C1 Q4
5 marks Easy -1.3
  1. Evaluate \((0.2)^{-2}\). [2]
  2. Simplify \((16a^{12})^{\frac{3}{4}}\). [3]
OCR MEI C1 Q8
5 marks Easy -1.3
  1. Evaluate \(9^{-\frac{1}{2}}\). [2]
  2. Simplify \(\frac{(4x^4)^3 y^2}{2x^4 y^5}\). [3]
OCR MEI C1 Q8
5 marks Easy -1.3
  1. Find the value of \(\left(\frac{1}{25}\right)^{-\frac{1}{2}}\). [2]
  2. Simplify \(\frac{(2x^2y^3z)^5}{4y^5z}\). [3]
AQA AS Paper 1 2023 June Q2
1 marks Easy -1.8
Identify the expression below which is equivalent to \(\left(\frac{2x}{5}\right)^{-3}\) Circle your answer. [1 mark] \(\frac{8x^3}{125}\) \quad \(\frac{125x^3}{8}\) \quad \(\frac{125}{8x^3}\) \quad \(\frac{8}{125x^3}\)
AQA Paper 2 2019 June Q2
1 marks Easy -1.8
Simplify \(\sqrt{a^{\frac{2}{3}} \times a^{\frac{2}{5}}}\) Circle your answer. [1 mark] \(a^{\frac{2}{15}}\) \quad \(a^{\frac{4}{15}}\) \quad \(a^{\frac{8}{15}}\) \quad \(a^{\frac{16}{15}}\)
AQA Paper 3 2021 June Q6
4 marks Standard +0.3
Given that \(x > 0\) and \(x \neq 25\), fully simplify $$\frac{10 + 5x - 2x^{\frac{1}{2}} - x^{\frac{3}{2}}}{5 - \sqrt{x}}$$ Fully justify your answer. [4 marks]
WJEC Unit 1 2023 June Q5
7 marks Moderate -0.8
Simplify the expression \(\sqrt[3]{512a^7} - \frac{a^{\frac{7}{2}} \times a^{-\frac{1}{3}}}{a^6}\). [4]
SPS SPS SM 2020 October Q1
2 marks Easy -1.8
Simplify fully the following expressions:
  1. \(\frac{7y^{13}}{35y^7}\) [1]
  2. \(6x^{-2} \div x^{-5}\) [1]
SPS SPS SM 2022 October Q1
2 marks Easy -1.8
Simplify \(\left(\frac{x^{12}}{16}\right)^{-\frac{3}{4}}\) [2]
SPS SPS SM 2024 October Q7
4 marks Moderate -0.8
Express \(\frac{a^{\frac{1}{2}} - a^{\frac{2}{3}}}{a^{\frac{1}{3}} - a}\) in the form \(a^m + \sqrt{a^n}\), where \(m\) and \(n\) are integers and \(a \neq 0\) or 1. [4]
SPS SPS SM 2025 October Q1
8 marks Easy -1.8
Express each of the following in the form \(px^q\), where \(p\) and \(q\) are constants.
  1. \(\frac{2}{\sqrt[3]{x}}\) [1]
  2. \((5x\sqrt{x})^3\) [1]
  3. \(\sqrt{2x^3} \times \sqrt{8x^5}\) [1]
  4. \(x^5(27x^6)^{\frac{1}{3}}\) [2]
OCR H240/02 2017 Specimen Q1
4 marks Easy -1.8
Simplify fully.
  1. \(\sqrt{a^3} \times \sqrt{16a}\) [2]
  2. \((4b^6)^{\frac{3}{2}}\) [2]