IGCSE Mathematics | Practice Test | 25 Questions
Write $5^3$ as a product of numbers.
State the zero index rule. Give one example to support your answer.
Complete the rule for a negative index: $a^{-n} = \ldots$
Find the value of $4^3$.
Find the value of $6^0$.
Find the value of $3^{-1}$.
Find the value of $7^{-2}$.
Write down the rule for multiplying two powers with the same base. Use the formula $a^m \times a^n = \ldots$
Write down the rule for dividing two powers with the same base. Use the formula $a^m \div a^n = \ldots$
Write down the power of a power rule. Use the formula $(a^m)^n = \ldots$
Simplify $a^3 \times a^5$.
Simplify $x^7 \div x^3$.
Simplify $(b^2)^4$.
Find the value of $2^{-3} \times 2^4$.
Find the value of $2^3 \div 2^4$.
Find the value of $(2^3)^2$.
Simplify $5^3 \times 5^{-2}$ and find its value.
Find the value of $10^{-2}$. Give your answer as a decimal.
Simplify $\dfrac{m^6}{m^2}$.
Find the value of $4^{-2}$.
Simplify $3^2 \times 3^{-5} \times 3^4$. Write your answer as a single power of 3, then find its value.
(a) Write $\dfrac{1}{32}$ as a power of 2.
(b) Write $\dfrac{1}{27}$ as a power of 3.
Find the value of $n$ such that $2^n = \dfrac{1}{8}$. Show your working.
(a) Simplify $(x^3)^2 \div x^4$.
(b) Find the value of your answer to part (a) when $x = 2$.
Show that $(2^{-3} \times 2^5)^2 = 16$. Show every step of your working.
