SPS SPS SM 2025 October — Question 1 8 marks

Exam BoardSPS
ModuleSPS SM (SPS SM)
Year2025
SessionOctober
Marks8
TopicIndices and Surds
TypeSimplify algebraic expressions with indices
DifficultyEasy -1.8 This is a routine algebraic manipulation question testing basic index laws and surds. All parts require straightforward application of standard rules (negative/fractional indices, power of a product, multiplication of surds) with no problem-solving or conceptual insight needed. The multi-part structure and 5 total marks indicate this is an accessible starter question, significantly easier than average A-level content.
Spec1.02a Indices: laws of indices for rational exponents

Express each of the following in the form \(px^q\), where \(p\) and \(q\) are constants.
  1. \(\frac{2}{\sqrt[3]{x}}\) [1]
  2. \((5x\sqrt{x})^3\) [1]
  3. \(\sqrt{2x^3} \times \sqrt{8x^5}\) [1]
  4. \(x^5(27x^6)^{\frac{1}{3}}\) [2]

Express each of the following in the form $px^q$, where $p$ and $q$ are constants.

\begin{enumerate}[label=(\alph*)]
\item $\frac{2}{\sqrt[3]{x}}$ [1]

\item $(5x\sqrt{x})^3$ [1]

\item $\sqrt{2x^3} \times \sqrt{8x^5}$ [1]

\item $x^5(27x^6)^{\frac{1}{3}}$ [2]
\end{enumerate}

\hfill \mbox{\textit{SPS SPS SM 2025 Q1 [8]}}