Test – C1.7 – Indices

IGCSE Mathematics  |  Practice Test  |  25 Questions

Instructions: Answer all 25 questions. Show your working where required. Write your answers in the spaces provided.
Section A — Recall
Questions 1–10   |   Write down the answer or state the rule
1.

Write $5^3$ as a product of numbers.

2.

State the zero index rule. Give one example to support your answer.

3.

Complete the rule for a negative index:   $a^{-n} = \ldots$

4.

Find the value of $4^3$.

5.

Find the value of $6^0$.

6.

Find the value of $3^{-1}$.

7.

Find the value of $7^{-2}$.

8.

Write down the rule for multiplying two powers with the same base. Use the formula $a^m \times a^n = \ldots$

9.

Write down the rule for dividing two powers with the same base. Use the formula $a^m \div a^n = \ldots$

10.

Write down the power of a power rule. Use the formula $(a^m)^n = \ldots$

Section B — Application
Questions 11–20   |   Show all working
11.

Simplify $a^3 \times a^5$.

12.

Simplify $x^7 \div x^3$.

13.

Simplify $(b^2)^4$.

14.

Find the value of $2^{-3} \times 2^4$.

15.

Find the value of $2^3 \div 2^4$.

16.

Find the value of $(2^3)^2$.

17.

Simplify $5^3 \times 5^{-2}$ and find its value.

18.

Find the value of $10^{-2}$. Give your answer as a decimal.

19.

Simplify $\dfrac{m^6}{m^2}$.

20.

Find the value of $4^{-2}$.

Section C — Challenge
Questions 21–25   |   Show all working clearly
21.

Simplify $3^2 \times 3^{-5} \times 3^4$. Write your answer as a single power of 3, then find its value.

22.

(a) Write $\dfrac{1}{32}$ as a power of 2.

(b) Write $\dfrac{1}{27}$ as a power of 3.

23.

Find the value of $n$ such that $2^n = \dfrac{1}{8}$. Show your working.

24.

(a) Simplify $(x^3)^2 \div x^4$.

(b) Find the value of your answer to part (a) when $x = 2$.

25.

Show that $(2^{-3} \times 2^5)^2 = 16$. Show every step of your working.

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