Test Questions
Try some of the following to test your skills:
Simplify, leaving your answer in index form:
| 1. | 73 x 7 = | 9. |
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| 2. | 56 x 52 = | 10. | 64 = |
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| 3. | 95 ÷ 90 = | 11. | 2−3 = | |||||||
| 4. | 35 ÷ 3-2 = | 12. | 5− |
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| 5. |
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13. | 4− |
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| 6. | (43)4 = | 14. |
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| 7. | 72 x 78 x 73 = | 15. | 9 ÷ 8 |
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| 8. | 312 x 35 ÷ 34 = |
Answers:
| 1. | 74 | 9. | 27 | ||
| 2. | 58 | 10. | 8 | ||
| 3. | 95 | 11. |
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| 4. | 37 | 12. |
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| 5. | 102 | 13. |
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| 6. | 47 | 14. |
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| 7. | 713 | 15. | 31 | ||
| 8. | 313 |
Remember the rules of indices:
Multiplying powers with the same base am x an = am+n
Dividing powers with the same base am ÷ an = am−n
Raising a power to a power (am)n = amn
Raising any number to the power zero a0= 1 (also a1= a)
| Negative powers and reciprocals | a−m = | 1 | (a−m is the reciprocal of am) |
| am |
Fractional powers and roots 
and 