AAT test 3: Rational Expressions, Exponents, & Radicals
solve: (sq. root of 5 - sq. root of 11)^2
16 - 2 * sq root of 55
solve: (4/9)^(1/2)
2/3
solve: 216^(2/3)
36
solve: (2^(1/2) - r^(-1/2))^2
4r- 4 + 1/r
factor given the common factor: 5r^-6 - 10r^-8; 5r^-8
5r^-8(r^2 - 2)
solve: 16^(3/4)
8
solve: [2/(x+2)]/[1/(x+2) + 2/x]
LCD: x(x+2) answer: (2x)/(3x+4)
informal definition of a rational function
a fraction whose numerator and denominator are polynomials
asymptote
a line the curve approaches but does not cross
3r + 1 is a... a. monomial b. binomial c. trinomial
b. binomial
BFF
best factored form
when solving complex fractions, find the LCD for....
both the numerator and the denominator
rational = ??
fractional
when solving for the LCD, always take the _________ __________
highest powers
technical definition of a rational function
let u(x) and v(x) be polynomial functions. the function f(x) = [u(x)]/[v(x)] is a rational function. the domain of f is the set of all real numbers for which v(x) is not equal to 0
radical law #4
mth root of the nth root of a = m*nth root of a
dividing is ___________ by the reciprocal
multiplying
what kind of exponents are acceptable in calc but not alg?
negative exponents (DON'T PUT THEM IN YOUR ANSWERS)
radical law #2
nth root of a*b = nth root of a * nth root of b
radical outlaw #1
nth root of a+b is not equal to nth root of a + nth root of b
radical outlaw #2
nth root of a-b is not equak to the nth root of a - nth root of b
radical law #3
nth root of a/b = nth root of a / nth root of b
radical law #5
nth root of a^m = a^(m/n)
radical law #1
nth root of a^n = a
a graph for degree 2's is what shape?
parabola
which law do you use to change an expression from radical form to exponential form?
radical law #5
when simplifying rational exponent expressions always ______________ _____________ first
subtract exponents
how do you know which form to give your answer in?
the form that the problem is given should be the way that your answer should be written
what drives the problem?
the index
T or F: LCD means the same thing as LCM
true
when u, v, w, and z are real numbers, variables, or algebraic expressions and v and z are not equal to 0... what statement is true?
u/v * w/z = (uw)/(vz)
why is "cancel like terms" wrong?
when referring to a sum, it's wrong because you can't cancel like terms in sums *YOU CAN ONLY CANCEL LIKE FACTORS*
domain: x or y values?
x values
range: x or y values??
y values
solve: (y^3 - 27)/(y-3)
y^2 + 3y + 9
why are the outlaws true?
you can't distribute a radical
what do you do to get rid of radicals in the denominator?
"rationalize the denominator" aka "rat the den"
when solving for radical expressions with decimals use...
# of decimal locations/index
solve: 2/(2x-3) - (3x)/(3-2x)
(3x+2)/(2x-3)
solve: (6x)/(x^2 - 4) + 3/(2-x)
(6x-3)/(x-2)
solve: sq. root of (81/16)
(81/16)^(1/2)
a^(m/n) = ?? = ??
(a^(1/n))^m = (a^m)^(1/n)
simplify: [3/(p^2 - 16) + p]/[1/(p-4)]
(p^3 - 16p + 3)/(p+4)
an expression is in BRF (best radical form) when...
- all possible factors have been removed from each radical - no denominator of a fraction contains a radical
what do you do if a negative exponent appears in an expression?
- factor out the lowest neg. exponent because it concentrates the neg. exponents in one place - if no neg. exponent occurs then just use regular factoring
radicals are LIKE when they have the same:
- index - radicand
when adding and subtracting rational expressions always:
- put your answer into lowest terms - state your answer in exact form (fractions NOT decimals)
solve: [(4x^2y)/(3xy^4)] * [(-6x^2y^2)/(10x)]
-4/(5xy); x and y are not equal to 0
solve: cubed root of 0.000343
0.07
solve: 4^0
1
solve: [(p^15 * q^12)^(-4/3)]/[(p^24 * q^16)^(3/4)]
1/(p^38 * q^30)