| Exam Board | SPS |
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| Module | SPS SM (SPS SM) |
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| Year | 2025 |
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| Session | October |
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| Topic | Indices and Surds |
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- Express each of the following in the form \(p x ^ { q }\), where \(p\) and \(q\) are constants.
- \(\frac { 2 } { \sqrt [ 4 ] { x } }\)
- \(\quad ( 5 x \sqrt { x } ) ^ { 3 }\)
- \(\sqrt { 2 x ^ { 3 } } \times \sqrt { 8 x ^ { 5 } }\)
- \(\quad x ^ { 5 } \left( 27 x ^ { 6 } \right) ^ { \frac { 2 } { 3 } }\)
- In this question you must show detailed reasoning.
Simplify \(10 + 7 \sqrt { 5 } + \frac { 38 } { 1 - 2 \sqrt { 5 } }\), giving your answer in the form \(a + b \sqrt { 5 }\).