In this question you must show detailed reasoning.
Express 273 27\sqrt{3}\,273 in the form 3a3^a3a, where a a\,a is a rational number.
Express 27+372\displaystyle \frac{2}{7}+\frac{3}{7}\sqrt{2}72+732 in the form ea−be\displaystyle \frac{\sqrt{e}}{a-b\sqrt{e}}a−bee, where a a\,a and b b\,b are integers and e e\,e is a prime number.
233 exam-style questions on Edexcel A Level Maths Algebraic Expressions, covering 1.1 Index Laws, 1.2 Expanding Brackets, 1.3 Factorising, 1.4 Negative and Fractional Indices, and 1.5 Surds. Each one has a worked solution and a mark scheme showing where the marks go.