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