Question 1
1 markEvaluate the value of \((-3)^4\).
IB Middle Years Programme (MYP) · Mathematics
Integer Exponents, Roots and Standard Form: Practice Questions
5 multiple-choice questions marked as you go, and 3 written questions with worked solutions. All on Integer Exponents, Roots and Standard Form.
8 questions20 marksFree, no account
Question 2
1 markSolve the exponential equation \(9^{x-1} = 27^{x+2}\) for \(x\).
Question 3
1 markIf \(5^x = 4\) and \(2^y = 125\), find the value of \(xy\).
Question 4
1 markFind the value of \(\sqrt{144} - \sqrt[3]{-64}\).
Question 5
1 markSimplify \(\dfrac{\left(3x^{-2}y^4\right)^{-2}}{9x^5 y^{-6}}\) and express your answer with positive indices.
Question 6
5 marksFind the value of \(n\) that satisfies the equation:
\(\sqrt{3^n \cdot \sqrt{3^n \cdot \sqrt{3^n}}} = 27\sqrt{3}\)
Write your answer out first, then check it against the worked solution.
Question 7
6 marksFind the value of \(x\) that satisfies the following equation:
\(\sqrt[3]{8^x \cdot 4^{x+1}} = 16\)
Write your answer out first, then check it against the worked solution.
Question 8
4 marksConsider the following numerical expressions involving powers and square roots.
(a) Evaluate the expression \( 3^4 - 2^5 \).
(b) Find the value of \( \sqrt{144} + \sqrt{25} \).
(c) Using your answers from (a) and (b), determine the value of \( (3^4 - 2^5) \times (\sqrt{144} + \sqrt{25}) \).
Write your answer out first, then check it against the worked solution.
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