Powers and Roots Flashcards
2^3
8
2^4
16
2^5
32
2^6
64
2^7
128
2^8
256
2^9
512
3^4
81
4^4
256
5^4
625
6^3
216
7^3
343
8^3
512
9^3
729
Positive base less than one
Gets smaller with increasing exponential growth
Negative base less than -1 (-3)
Absolute powers getting bigger but signs are alternating
Number between 0 and 1
Values getting smaller but signs are alternating and we are APPROACHING 0
-n^even exponent
Even number
No exponent law for
The sum or difference of powers so a raised to something plus b raised to something
(AB)^n
A^n * b^n
Same for division
(A+B)^n
Not equal to A^n +B^n
If two bases are equal
Exponents can be solved for
What is the units digit?
Repeating pattern include the first number write from the first number
Period of the pattern (usually 4) pattern
7,9,3,1 4th is 1 so 120th is 1
If radical sign is given
Positive square root
Square root of 2
1.4
Square root of 3
1.7
Square root of 5
2.2
If b is between 0 and 1 then
B is greater than b squared and the square root of b is greater than 6
Higher order closer result to 1
Normal numbers get smaller closer to 1
Numbers between 0 and 1 get bigger and move to 1
14 squared
196
15squared
225
Can you dist an exponent over number radical composition
Yes; if raised to 4= 2^^2
Even power
Perfect square
Extraneous roots
Negative numbers; don’t always give roots that will work; **
radical
isolate and then square
square root of something always
Positive
2^(a/b)
(2^a)root b or( rootbof 2)*a
We can take negative roots only of
Odd numbers
When bases are equal
exponent are equal; can write 16 and 32 as powers of 2
Expression with a square root
opposite number signs
If vsquared= 2ad; if v triples and a doubles then d is what*; video working with formula
Set all equal to 1 v=2=a=d=1; now when v triples its 3 and when a doubles its two so the number is vsquared over 2a= 9 over 2; 2=1 because its a ratio so doesnt really matter; so what is d multipled by, isolate d
