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Finding powers of fractions is simple if we change the powers into multiplications.
We can either multiply the top numbers together and then the bottom numbers together, remembering to reduce the final answer, or we can cancel down within the calculation if possible.
Example
Work out
Answer
Expand the power to create a multiplication.
Here the power of 4 means we multiply the fraction by itself 4 times.
| 3 | × | 3 | × | 3 | × | 3 |
| 10 | 10 | 10 | 10 |
| = | 3 × 3 × 3 × 3 |
| 10 × 10 × 10 × 10 |
OR
| = | 34 |
| 104 |
| = | 81 |
| 10,000 |
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