Powers and roots

Write these values in ascending order, beginning with the smallest: $2^{5},\;5^{2},\;\sqrt[3]{1000},\;27^{0}$.

May/June 2016

Evaluate $3^3 - 3^0$ to find the result.

May/June 2018

Calculate the value of $(\sqrt{9}\times\sqrt[3]{64})^2$.

May/June 2022

Evaluate the value of $125^{\tfrac{1}{3}}$.

May/June 2024

Evaluate the value of $\sqrt[3]{125}$.

May/June 2025

Evaluate the value of $3^2+3^1+3^0$.

Oct/Nov 2016

This table lists square roots, correct to $4$ significant figures, for a selection of numbers from $31.0$ up to $32.9$.

Oct/Nov 2017

Evaluate the expression $9^2-9^0$.

Oct/Nov 2017

Evaluate the expression $\left(\frac{1}{3}\right)^{0} - \left(\frac{1}{3}\right)^{2}$.

Oct/Nov 2018

Evaluate the value of $\sqrt{4900}$.

Oct/Nov 2021

Write $4 \times 4 \times 4 \times 4 \times 4$ in index form using base $4$.

Oct/Nov 2022

Work out the value of $80 \div 0.02$.

Oct/Nov 2022

Simplify the expression $(x^2)^3$.

Oct/Nov 2022

Evaluate the expression $4^2 + \sqrt[3]{27}$.

Oct/Nov 2023

Find the decimal that is exactly midway between $\frac{3}{5}$ and $68\%$.

Oct/Nov 2023

Write $360$ as a product of primes.

Oct/Nov 2024

Calculate $\frac{12-\sqrt[3]{6}}{0.3^2}$. Give your answer correct to 2 decimal places.

Oct/Nov 2025