Exponents (indices)
An exponent tells us how many times a number is multiplied by itself. In the base is 2 and the exponent is 4, so .
| Law | Rule | Example |
|---|---|---|
| Multiply | a^m × a^n = a^(m+n) | 2³ × 2⁴ = 2⁷ |
| Divide | a^m ÷ a^n = a^(m−n) | 5⁶ ÷ 5² = 5⁴ |
| Power of a power | (a^m)^n = a^(mn) | (3²)³ = 3⁶ |
| Zero | a⁰ = 1 | 7⁰ = 1 |
| Negative | a^(−n) = 1 ÷ a^n | 2⁻³ = 1/8 |
Try itCheck the multiplication law
Choose a base and two exponents. The product of the powers always equals the base raised to the sum of the exponents.
Worked exampleSimplify with the laws
Simplify .
- Add exponents on top.
- Subtract the bottom exponent.
Answer:
Radicals (roots)
A radical is a root. because . A root that is not a whole number, such as , can often be simplified by pulling out a perfect square.
Changing the subject of a formula
Transposition means rearranging a formula to make a different letter the subject. Undo the operations in reverse order, doing the same to both sides.
Worked exampleMake r the subject
Make the subject of .
- Divide both sides by π.
- Take the square root.
Answer:
Key terms
- Exponent
- How many times the base is multiplied by itself.
- Base
- The number being multiplied.
- Radical
- A root such as a square root.
- Transposition
- Rearranging a formula to make another letter the subject.
Summary
- Same base: add exponents to multiply, subtract to divide.
- a⁰ = 1 and a⁻ⁿ = 1/aⁿ.
- Simplify roots by taking out perfect squares: √12 = 2√3.
- To change the subject, undo operations in reverse order on both sides.