Numeracy · Guided Practice

Indices

13 questions with answers and video solutions. Try each one before revealing the answer.

1
2014 P2 Q8
3 Marks
Simplify n5×10n2n2\displaystyle \large\frac{n^5 \times 10n}{2n^2}.
2
2015 P1 Q14
2 Marks
Evaluate 853.\displaystyle 8^{\frac53}.
3
2016 P2 Q10
3 Marks

Simplify (n2)3×n−10\displaystyle (n^{2})^{3}\times n^{-10}.
Give your answer with a positive power.

4
2017 P2 Q12
2 Marks

Express 1x3\displaystyle \frac{1}{\sqrt[3]{x}} in the form xn.\displaystyle x^{n}.

5
2018 P1 Q15
2 Marks

Remove the brackets and simplify (23p4)2\displaystyle (\frac{2}{3}p^{4})^{2}.

6
Simplify, expressing your answer with a positive power
(23p−4)2.\displaystyle \left(\frac{2}{3}p^{-4}\right)^2.

No hints on this one — its full written solution is with the answer.

7
2019 P2 Q16
3 Marks

Simplify a4×3aa.\displaystyle \frac{a^{4}\times3a}{\sqrt{a}}.

8
2021 P1 Q15
Evaluate 1632.\displaystyle 16^{\frac32}.

No hints on this one — its full written solution is with the answer.

9
2022 P1 Q11
3 Marks

Simplify (m−2)4×m−5\displaystyle (m^{-2})^{4} \times m^{-5}.
Give your answer with a positive power.

10
2023 P1 Q12
3 Marks
Simplify 5c−2c3×c4.\displaystyle \large\frac{5c^{-2}}{c^3 \times c^4}.
Give your answer with a positive power.
11
2024 P1 Q13
2 Marks
Expand and simplify fully x(x12+x−1).\displaystyle x(x^{\frac{1}{2}}+x^{-1}).
12
2025 P1 Q10
3 Marks
Simplify n7×(n3)2n4.\displaystyle \frac{n^{7}\times(n^{3})^{2}}{n^{4}}.
13
2026 P2 Q11
3 Marks
Simplify a17(3a4)3.\displaystyle \frac{a^{17}}{(3a^{4})^{3}}.

Keep practising

More indices questions

New questions, modelled on past paper questions and checked against their marking instructions. Not reprints — you have not seen these before.

Practice questions courtesy of Maths.scot. Full written solutions are on his site — the links above go straight to them.

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