Mathematics 0580 · IGCSE
Indices I
83 practice questions on Indices I, with worked solutions and instant marking.
$2^{p}=\frac{1}{8^{4}}$
Feb/March 2018
Simplify $5 \times x^0$.
Feb/March 2020
Work out $x^{12} \div x^3$.
Feb/March 2021
Simplify $(343x^{9})^{\frac{2}{3}}$.
Feb/March 2021
State the value of $h$.
Feb/March 2024
Simplify the expression $\left(\dfrac{x^2}{4}\right)^{\frac{3}{2}}$.
Feb/March 2025
Simplify $5x^0$.
May/June 2015
Simplify $12x^{12} \div 3x^3$.
May/June 2015
Calculate $(2.1 - 0.078)^{17}$, and give your answer correct to 4 significant figures.
May/June 2016
Calculate $(2.1 - 0.078)^{17}$, and give your answer accurate to 4 significant figures.
May/June 2016
Write the decimal form of $5^{-3}$.
May/June 2017
Simplify the expression $(x^2)^5$.
May/June 2017
Simplify the expression $\left(x^2\right)^5$.
May/June 2017
For $2^r = \frac{1}{16}$, find the value of $r$.
May/June 2017
Simplify the expression $6w^{0}$.
May/June 2017
Simplify the expression $(x^3)^4$.
May/June 2018
Determine the value of $p$ when $5^p \div 5^8 = 5^{13}$.
May/June 2018
Work out the value of $4^{-2}$.
May/June 2018
$3^{-q} \times \frac{1}{27} = 81$. Find the numerical value of $q$.
May/June 2018
Simplify the expression $(3p^2)^5$.
May/June 2018
Simplify the expression $t^{21} \div t^{7}$.
May/June 2019
Simplify the expression $5m^2 \times 2m^3$.
May/June 2019
Simplify the expression $(81y^{16})^{\frac{3}{4}}$.
May/June 2019
Simplify the expression $t^{21} \div t^{7}$.
May/June 2019
Simplify this expression.
May/June 2019
Write $\dfrac{1}{2\times2\times2\times2\times2}$ in the form of a power of 2.
May/June 2021
The equation $7^{x} \div 7^{4} = 7^{9}$ is provided.
May/June 2021
Simplify $3x^3 \times 4x^4$ by applying index laws.
May/June 2021
Simplify $3x^3 \times 4x^4$.
May/June 2021
Calculate the value of $4^5 - 5^4$.
May/June 2022
$9^x \times 9^2 = 9^{12}$
May/June 2022
Simplify the expression $y^3 \div y^5$.
May/June 2022
$4^x=\dfrac{1}{64}$
May/June 2022
Determine $p$ in $6^p \times 6^4 = 6^{28}$.
May/June 2022
Using the relation $m^{-\frac{1}{4}} = 27m^{-1}$, find the value of $m$.
May/June 2022
Simplify the expression $y^3 \div y^5$.
May/June 2022
Simplify the expression $18x^{12} \div 3x^{3}$.
May/June 2023
Simplify the expression $d^8 \div d^2$.
May/June 2023
Simplify the expression $d^8 \div d^2$.
May/June 2023
Find $137^0$.
May/June 2024
The equation $5^7 \div 5^x = 5^3$ is provided.
May/June 2024
Using $3^p \times 3^4 = 3^{10}$, find the value of $p$.
May/June 2025
Find the reciprocal value of $\frac{1}{3}$.
May/June 2025
Simplify this expression.
May/June 2025
Simplify $\dfrac{r^6}{r^2}$.
Oct/Nov 2015
Simplify $\left(\frac{x^{64}}{16y^{16}}\right)^{\frac{1}{4}}$.
Oct/Nov 2015
Simplify $n^2 \times n^5$.
Oct/Nov 2016
Write $5^{-3}$ in fractional form.
Oct/Nov 2016
Simplify the expression $36y^5 \div 4y^2$.
Oct/Nov 2016
Find the simplified form of $n^2 \times n^5$.
Oct/Nov 2016
Simplify the expression $(m^{5})^{2}$.
Oct/Nov 2017
Find the value of $2^{-4} \times 2^{5}$.
Oct/Nov 2017
Simplify the expression $y^4 \times y^5$.
Oct/Nov 2017
Work out $(m^{5})^{2}$.
Oct/Nov 2017
Calculate $2^{-4} \times 2^{5}$.
Oct/Nov 2017
Calculate $\sqrt{9 + 25^{-\frac{1}{3}}}$.
Oct/Nov 2017
$(\sqrt[3]{10})^2 = 10^p$. Calculate the value of $p$.
Oct/Nov 2017
Calculate the value of $\frac{a^5}{a^2}$.
Oct/Nov 2018
From $t^x \times t^2 = t^{10}$, determine the value of x.
Oct/Nov 2018
Calculate the value of $0.125^{-\frac{2}{3}}$.
Oct/Nov 2018
Simplify the expression $\dfrac{w^2}{w^3}$.
Oct/Nov 2018
Calculate $\left(\dfrac{125}{27}\right)^{-\frac{2}{3}}$.
Oct/Nov 2018
Simplify the expression $2x^3 \times 3x^2$.
Oct/Nov 2019
Find the value obtained from $6^0 + 6^2$.
Oct/Nov 2019
In $x^{3} \times x^{6} = x^{m}$, determine the value of $m$.
Oct/Nov 2019
Simplify the expression $2x^{2} \times 5x^{5}$.
Oct/Nov 2020
Simplify the expression $(4xy^2)^3$.
Oct/Nov 2020
Simplify the expression $a^2 \div a^6$.
Oct/Nov 2020
Simplify the expression $\dfrac{x^{2/3}}{x^{8/3}}$.
Oct/Nov 2021
Write $243 \times 27^{2n}$ in the form of one power of 3, expressed using $n$.
Oct/Nov 2021
Simplify the expression. $32g^{32} \div 4g^{4}$
Oct/Nov 2021
$5^8 \div 5^x = 5^2$. Determine the value of $x$.
Oct/Nov 2022
For $120 = 2^m \times 3 \times 5$, find $m$.
Oct/Nov 2022
Simplify: $18x^{18} \div 9x^{9}$.
Oct/Nov 2022
Using the equation $3^{3p} \times 3^{2p} = 729$, find the value of $p$.
Oct/Nov 2023
Aneel starts with 80 tea bags, $\frac{1}{2}$ kg of sugar and 1 litre of milk. For each cup of tea, he uses: • 1 tea bag • 8 grams of sugar • 40 millilitres of milk.
Oct/Nov 2023
Find the value of $2^5$
Oct/Nov 2025
Calculate the value of $5^{-5} \times 5^{5}$.
Oct/Nov 2025
\(M=2^7\times3^3\times5^2\)
Oct/Nov 2025
Determine the value of $3^2 \div 3^{-2}$.
Oct/Nov 2025
Write down the value of $73^0$.
Oct/Nov 2025
$n^{15}\div n^x=n^5$
Oct/Nov 2025
Calculate the value of $8^5$. Give your answer correct to 3 significant figures.
Oct/Nov 2025