Download Fractional and negative indices

Fractional indices & roots
Grade A at GCSE (you can do it!)
What are two square roots
multiplied together?
•
•
•
•
•
What is √4 x √4?
2x2=4
What is √25 x √25?
5 x 5 = 25
If you multiply two square roots together,
you get the number itself
So what power is a square root?
• What is 41/2 x 41/2?
• 41 or just 4, because ½ + ½ = 1 (remember
to add the powers when multiplying
identical base numbers with indices)
• Because of this fact, it has been decided
that the power of a half is the square root
• So 41/2 means √4
• So 41/2 = 2. Make up your own example.
What power is a cube root?
•
•
•
•
•
What is 3√8 x 3√8 x 3√8?
2x2x2=8
What is 81/3 x 81/3 x 81/3?
81 or just 8
So the power of a third is the power for a
cube root
• So 81/3 = 3√8 = 2
• What could you say is the general rule?
The general rule is
1
n
a  a
n