Powers, Roots and Surds
Indices
Pearson Edexcel International GCSE Mathematics A
Index laws
| Law | Form |
|---|---|
| Multiplying powers of the same base | am × an = am + n |
| Dividing powers of the same base | am ÷ an = am − n |
| Power of a power | (am)n = amn |
- To find an unknown power, write each side as a single power of the same base, then equate the powers.
- Write every step as a power of the base. Never write a calculator value of each side.
Zero, negative and fractional powers
| Power | Form |
|---|---|
| Zero | a0 = 1 |
| Negative | a−n = 1an |
| Square root | √a = a1/2 |
| Unit fraction | a1/n = n√a |
| Fraction | am/n = (n√a)m |
- A bracket to the power 0 is 1: (…)0 = 1.
- A number multiplying the bracket is not raised to the power 0: k × (…)0 = k.
Writing numbers as powers of one base
Method: find the power of a prime base
- Write each number as a power of the prime base.
- Write each root as a fractional power.
- Apply the index laws to reach one power of the base.
- Equate the powers and give the value of n as a fraction.
Worked example: write every term as a power of one base, then find n
3√3 × 94 ÷ 274/3 = 3n
Work out the value of n. Show your working clearly.
3√3 = 31/3, 94 = 38, 274/3 = 34
31/3 × 38 ÷ 34 = 313/3
n = 133
- When the answer is asked in the form 2a, write the whole power 2a.
- To find a base from its power, raise both sides to the reciprocal of the power.
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