Radical Functions and Rational Exponents Flashcards
Properties of exponents: a^0=
a≠
1
0
Properties of exponents: a^m/a^n=
a^m-n
Properties of exponents: a^-n=
1/a^n
Properties of exponents: (ab)^n=
a^nb^n
Properties of exponents: a^m X a^n=
a^m+n
Properties of exponents: (a/b)^n=
a^n/b^n
There is one real nth root of b, denoted to radical form n√b when
n is odd
There are two real nth roots of b when b is positive and
n is even.
When the n is even and b is positive, the positive root is the … and its symbol is .
The negative root is its ________, or .
principal root.
n√b.
opposite
-n√b.
When n is even and b is negative, there are
no real nth roots of b.
What is the only nth root of 0?
0
If you write the √ sign, then you add
±
If the √ sign is already written, then it is
only +
When simplifying, there are none of these types of answers:
No decimal answers
What shows how many to find (and group)?
Index
What does n√a X n√b =, according to the combining radical expressions products property?
n√ab
What does n√a / n√b =, according to the combining radical expressions quotients property?
n√a/b
What can be used to separate the index and exponent in an expression?
Parentheses
What happens with the phrase, “The grass is always greener on the other side?”
The negative signs fall off the numbers when they move over the fraction.
What is the phrase that goes with the negative signs falling off when they mover over the fraction?
“The grass is always greener on the other side.”
If there is an even index, what does the answer receive?
±
Imaginary numbers (i) only show up in what types of problems?
Problems with square roots.
If the exponent is greater than 5…
It’s not worth writing the long answer.
If the exponent is greater than 5, it’s not worth writing the long answer unless
the base is small.
