Evaluate numerical powers

A question is this type if and only if it asks to evaluate a specific numerical expression involving powers or roots with no algebraic variables, such as 16^(1/2), 81^(3/4), or (1/25)^(-1/2).

45 questions · Easy -1.6

1.02a Indices: laws of indices for rational exponents
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OCR MEI C1 2011 June Q3
5 marks Easy -1.3
  1. Evaluate \(\left(\frac{9}{16}\right)^{-\frac{1}{2}}\). [2]
  2. Simplify \(\frac{(2ac^2)^3 \times 9a^2c}{36a^4c^{12}}\). [3]
OCR MEI C1 2012 June Q3
4 marks Easy -1.8
  1. Evaluate \(\left(\frac{1}{5}\right)^{-2}\). [2]
  2. Evaluate \(\left(\frac{8}{27}\right)^{\frac{2}{3}}\). [2]
Edexcel C1 Q1
4 marks Easy -1.8
  1. Express \(\frac{21}{\sqrt{7}}\) in the form \(k\sqrt{7}\). [2]
  2. Express \(8^{-1}\) as an exact fraction in its simplest form. [2]
Edexcel C1 Q1
3 marks Easy -1.8
Evaluate \(49^{\frac{1}{2}} + 8^{\frac{1}{3}}\). [3]
OCR C1 Q1
4 marks Easy -1.8
  1. Express \(\frac{21}{\sqrt{7}}\) in the form \(k\sqrt{7}\). [2]
  2. Express \(8^{-1}\) as an exact fraction in its simplest form. [2]
OCR C1 Q1
3 marks Easy -1.8
Evaluate \(49^{\frac{1}{2}} + 8^{\frac{2}{3}}\). [3]
OCR MEI C1 Q1
4 marks Easy -1.3
Evaluate the following.
  1. \(200^0\) [1]
  2. \(\left(\frac{25}{9}\right)^{-\frac{1}{2}}\) [3]
OCR MEI C1 Q2
5 marks Easy -1.3
  1. Evaluate \(\left(\frac{1}{27}\right)^{\frac{2}{3}}\). [2]
  2. Simplify \(\frac{(4a^2c)^3}{32a^4c^7}\). [3]
OCR MEI C1 Q5
4 marks Easy -1.8
Find the value of each of the following.
  1. \(\left(\frac{5}{3}\right)^{-2}\) [2]
  2. \(81^{\frac{1}{4}}\) [2]
OCR MEI C1 Q6
4 marks Easy -1.8
  1. Evaluate \(\left(\frac{1}{5}\right)^{-2}\). [2]
  2. Evaluate \(\left(\frac{8}{27}\right)^{\frac{2}{3}}\). [2]
OCR MEI C1 Q10
5 marks Easy -1.3
  1. Evaluate \(\left(\frac{9}{16}\right)^{-\frac{1}{2}}\). [2]
  2. Simplify \(\frac{(2ac^2)^3 \times 9a^2c}{36a^4c^{12}}\). [3]
OCR MEI C1 Q11
4 marks Easy -1.8
  1. Write down the value of each of the following.
    1. \(4^{-2}\) [1]
    2. \(9^0\) [1]
  2. Find the value of \(\left(\frac{64}{125}\right)^{\frac{4}{3}}\). [2]
OCR MEI C1 Q2
5 marks Easy -1.8
  1. Simplify \((5a^2b)^2 \times 2b^4\). [2]
  2. Evaluate \(\left(\frac{4}{16}\right)^{-1}\). [1]
  3. Evaluate \((16)^{\frac{3}{2}}\). [2]
OCR MEI C1 Q5
3 marks Easy -1.8
Find the value of each of the following.
  1. \(5^2 \times 5^{-2}\) [2]
  2. \(100^{\frac{1}{2}}\) [1]
OCR MEI C1 Q6
2 marks Easy -2.0
State the value of each of the following.
  1. \(2^{-3}\) [1]
  2. \(9^0\) [1]
OCR MEI C1 Q9
4 marks Easy -1.8
  1. Write down the value of \(\left(\frac{1}{4}\right)^0\). [1]
  2. Find the value of \(16^{-\frac{3}{2}}\). [3]
OCR MEI C1 Q10
4 marks Easy -1.8
  1. Find \(a\), given that \(a^3 = 64x^{12}y^3\). [2]
  2. Find the value of \(\left(\frac{1}{2}\right)^{-5}\). [2]
OCR MEI C1 Q11
4 marks Easy -1.8
Find the value of each of the following, giving each answer as an integer or fraction as appropriate.
  1. \(8^{\frac{1}{3}}\) [2]
  2. \(\left(\frac{7}{3}\right)^{-2}\) [2]
OCR MEI C1 Q13
5 marks Easy -1.3
Simplify the following.
  1. \(\frac{16^{\frac{1}{3}}}{81^{\frac{1}{4}}}\) [2]
  2. \(\frac{12(a^3b^2c)^4}{4a^2c^6}\) [3]
SPS SPS SM 2023 October Q1
3 marks Easy -1.2
In this question you must show detailed reasoning. Find the smallest positive integers \(m\) and \(n\) such that \(\left(\frac{64}{49}\right)^{-\frac{3}{2}} = \frac{m}{n}\) [3]