Mathematics 0580 · IGCSE
Indices II
37 practice questions on Indices II, with worked solutions and instant marking.
Find the value of $t^{24} \div t^4$.
Feb/March 2017
Simplify the expression $(y^5)^3$.
Feb/March 2019
Find $n$ for which $5^n = \frac{1}{125}$.
Feb/March 2019
Solve $\frac{x}{3} = 18$.
Feb/March 2025
Simplify the expression $6uw^{-3} \times 4uw^{6}$.
May/June 2015
Simplify $6uw^{-3} \times 4uw^6$.
May/June 2015
$8^{\frac{1}{x}} = 3$. Determine the value of $x$.
May/June 2015
Simplify the expression \(\left(\frac{1}{2}x^{\frac{2}{3}}\right)^3\).
May/June 2016
Simplify the expression $(32x^{10})^{\frac{3}{5}}$.
May/June 2016
Work out $x$ from $3^x = 243$.
May/June 2016
Simplify $(16x^{16})^{\frac{3}{4}}$ into its simplest form.
May/June 2017
Solve this equation. $5x - 17 = 7x + 3$.
May/June 2019
Express $(4ab^5)^4$ in simplest form.
May/June 2021
$7^5\times7^6$
May/June 2021
Simplify completely $(216x^{216})^{\frac{2}{3}}$.
May/June 2022
Simplify the expression $(81x^{12})^{\frac{3}{4}}$.
May/June 2023
Simplify $\frac{32g^{16}}{16g^8}$.
May/June 2024
Determine the value of
May/June 2025
Work out the lowest common multiple (LCM) of $15xy^3$ and $18x^4y$.
May/June 2025
$\dfrac{16^{5m}}{4} = 64^{2n}$ Find $m$ in terms of $n$.
May/June 2025
$10^k = \sqrt{\dfrac{10^{400}}{10^{220} \times 10^{80}}}$.
May/June 2025
Simplify $5x^5y \times 7x^3y^2$.
May/June 2025
Calculate the value of $2^{0.7}$.
Oct/Nov 2015
Simplify the expression $81^{\frac{3}{4}}$.
Oct/Nov 2017
Simplify $\left(\frac{x^3}{8}\right)^{\frac{4}{3}}$.
Oct/Nov 2019
Simplify the expression $2x^3 \times 3x^2$.
Oct/Nov 2019
From $3^{-2} \times 3^x = 81$, determine the value of $x$.
Oct/Nov 2019
Simplify completely. $(243y^{10})^{\frac{3}{5}}$
Oct/Nov 2021
Write $(81x^{16})^{\frac{3}{4}}$ in simplest form.
Oct/Nov 2022
Simplify $p^3 \times p^{11}$ fully.
Oct/Nov 2022
Simplify this expression.
Oct/Nov 2023
Simplify the expression $n^5 \times n$.
Oct/Nov 2023
Determine the lowest common multiple (LCM) for $12x^8$ and $8x^{12}$.
Oct/Nov 2023
Simplify the expression $\dfrac{18x^6}{3x^2}$.
Oct/Nov 2024
Simplify the expression $18x^{18} \div 3x^3$.
Oct/Nov 2024
Solve for $x$ in $\left(\frac{1}{3}\right)^x=9^{x+4}$.
Oct/Nov 2025
$27^{nx}=(9^x)^2$
Oct/Nov 2025