## Exam-Style Questions on Indices## Problems on Indices adapted from questions set in previous exams. |

## 1. | GCSE Higher |

Without using a calculator, show clearly that \(27^{\frac23}\) is equal to \(9\).

## 2. | GCSE Higher |

Work out the exact value of \(n\).

## 3. | GCSE Higher |

(a) The \(n\)th term of a sequence is \(2^n+2^{n+1}\)

Work out the 8th term of the sequence.

(b) The \(n\)th term of a different sequence is \(9(3^n + 3^{n+1})\)

Expand and express this expression as the sum of two powers of three.

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