Indices and Standard Form practice questions

Secondary 3 topics from the O-Level Mathematics 4052 syllabus. Every question below has a full worked solution.

When a student gets a question wrong in Math Amigo, it does not show the answer straight away. It reads the working, identifies the step that went wrong, and asks a question that points at the correction. The worked solution is there once a genuine attempt has been made.

Practise indices and standard form free

What this topic covers

Worked examples

Example 1

Simplify (a4b2)3÷a14(a^{4}b^{2})^{3} \div a^{14}. Express your answer with positive indices.
Show the worked solution
  • $(a^{4}b^{2})^{3} \div a^{14}$
  • $= a^{12} \cdot b^{6} \div a^{14} \quad \scriptsize\textit{Laws 3 \& 4: expand bracket}$
  • $= a^{-2} \cdot b^{6} \quad \scriptsize\textit{Law 2: subtract indices}$
  • $= \frac{b^{6}}{a^{2}} \quad \scriptsize\textit{Law 5: positive indices}$

Answer: b6/a2b^6/a^2

Example 2

Evaluate (−64)13(-64)^{\frac{1}{3}} without a calculator.
Show the worked solution
  • $(-64)^{\frac{1}{3}}$
  • $= \sqrt[3]{-64} \quad \scriptsize\textit{fractional index with odd root}$
  • $= -\sqrt[3]{64}$
  • $= -4$

Answer: −4-4

Example 3

Solve 5x+1=1255^{x + 1} = 125.
Show the worked solution
  • $5^{x + 1} = 125$
  • $5^{x + 1} = 5^{3} \quad \scriptsize\textit{express 125 as a power of 5}$
  • $x + 1 = 3 \quad \scriptsize\textit{equate exponents}$
  • $x = 3 - 1$
  • $x = 2$

Answer: 22

Questions parents ask

Is it really free?

The free plan is permanent and does not ask for a card. It has daily limits on the AI feedback, and the paid plans lift them.

Which syllabus does this follow?

O-Level Mathematics (4052), for Singapore secondary students. Math Amigo covers Secondary 1 to 4, both O-Level Mathematics and Additional Mathematics.

Will it just show my child the answer?

No. On a wrong answer it looks at the working, points to the step that went wrong, and asks a question that helps the student find the correction. The full worked solution is available after a genuine attempt.

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