Indices and Surds Flashcards
(12 cards)
Index Law 1
a^m x a^n = a^m+n
Law of Multiplication
If we multiply indices with the same base, we add the powers together.
Index Law 2
a^m/a^n = a^m-n
Law of Division
If we divide indices with the same base, we subtract the powers together.
Index Law 3
(a^m)^n = a^mn
Powers to a power
When powers are being put to powers, you multiply the indices.
Index Law 4
x ^ 0 = 1
Zero Power Law
Anything except 0 to the power of 0 is 1.
Index Law 5
(a^1 x b^1)^m
= a^m x b^m
Powers with Brackets
Powers outside of the bracket, get multiplied to the powers inside the bracket.
Index Law 6
Powers with Fractions
The power gets multiplied into the powers of the numerator and the denominator.
Negative Indices
a^-m = 1/a^m (written as a fraction)
If you want to change the sign, flip the side OR change the sign, cross the line.
Only the number/letter with the negative power changes sides.
Fractional Indices
n^√ x = x 1/n
Fractional powers can be rewritten as roots.
The nth root becomes the denominator.
Significant Figures
A way of rounding that makes data more accessible to the public.
Greater that 1:
SF are counted from left to right. Look at the number after the needed SF and round up or stay. Everything after the wanted SF, make everything 0.
Less that 1:
SF are counted from left to right starting at the first non 0 number. Repeat same steps.
Multiplying Surds
√a x √b = √ab
Any surd can be multiplied together by multiplying the co-efficient, multiplying the surd and simplifying if needed.
Simplifying Surds
Split the number in the root into the highest perfect square and its factor, e.g.
√250 = √(25 × 10) = 5√10
What is a surd?
A number under the square root symbol that’s answer isn’t a whole number/perfect square.
