In this question you must show detailed reasoning.
Express 792\displaystyle 7^{\frac{9}{2}}729 in the form aba\sqrt{b}ab, where a a\,a is an integer and b b\,b is a prime number.
Express 74−27\displaystyle \frac{\sqrt{7}}{4-2\sqrt{7}}4−277 in the form c+dec+d\sqrt{e}c+de, where c c\,c and d d\,d are rational numbers and e e\,e is a prime number.
134 exam-style questions on Edexcel AS 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.