Indices II: past paper questions

Where the questions come from

• Question 20May/June 2026, paper 21Structured4 marks

  Find the value of ${27}^{-\frac{2}{3}}\times (6^4{)}^{0.5}$.

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• Question 19Oct/Nov 2025, paper 21Structured3 marks

  Solve. $${\left(\frac{1}{3}\right)}^x=9^{x+4}$$ Solve.

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• Question 17Oct/Nov 2024, paper 23Structured4 marks

  Simplify. $18x^{18}÷3x^3$

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• Question 10Oct/Nov 2023, paper 21Structured5 marks

  Simplify. $n^5\times n$

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• Question 24May/June 2026, paper 22Structured3 marks

  $7^{2x+1}={49}^{2-x}$ Find the value of $x$.

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• Question 14Oct/Nov 2025, paper 22Structured4 marks

  Find the value of $3^2÷3^{-2}$

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• Question 13Oct/Nov 2023, paper 22Structured4 marks

  $3^{3p}\times 3^{2p}=729$ Find the value of $p$.

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• Question 22May/June 2026, paper 23Structured6 marks

  Simplify. $$(10b^4{)}^{-3}$$

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• Question 24Oct/Nov 2025, paper 22Structured2 marks

  ${27}^{nx}=(9^x{)}^2$ Find the value of $n$.

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• Question 17Oct/Nov 2023, paper 23Structured4 marks

  Simplify. $$(64y^{27}{)}^{\frac{2}{3}}$$

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• Question 9Oct/Nov 2025, paper 23Structured1 mark

  $n^{15}÷n^x=n^5$ Find the value of $x$.

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• Question 3May/June 2024, paper 41Structured13 marks

  $C=\frac{1}{4}x{y}^2$ Find $C$ when $x=5$ and $y=8$.

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• Question 6Oct/Nov 2025, paper 43Structured3 marks

  Simplify. $$\frac{y^5}{y^2}$$

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• Question 13Oct/Nov 2025, paper 43Structured3 marks

  The point $(5,1024)$ lies on the curve $y=c^x$, where $c$ is a whole number. Find the $y$-coordinate of the point on the curve with $x$-coordinate $-2$.

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• Question 17May/June 2023, paper 21Structured2 marks

  Simplify $(81x^{12}{)}^{\frac{3}{4}}$.

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• Question 19May/June 2025, paper 21Structured2 marks

  Find the value of ${27}^{-\frac{2}{3}}$.

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• Question 5May/June 2023, paper 23Structured1 mark

  Simplify $d^8÷d^2$.

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• Question 17May/June 2025, paper 22Structured4 marks

  Find the value of ${125}^{\frac{2}{3}}$

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• Question 9May/June 2023, paper 42Structured15 marks

  Simplify. $(3x^2{y}^4{)}^3$

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• Question 21May/June 2025, paper 42Structured4 marks

  Simplify. $$3t^5\times 5t^3$$

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• Question 9May/June 2025, paper 43Structured3 marks

  Simplify. $$5x^{5}y\times 7x^3{y}^2$$

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