unit 7-8 test

Question 1

reminders for 7.1

Answer 1

if answers are said to be all real numbers, and there is a -, then it’s not a real number

to find the domain of f(x), set the inside of the radical to >_ 0, flip sign if divided by negative

write answer as interval notation:
[-4, infinity) -with solution sets

Question 2

7.2- Fractional Exponents

Answer 2

when facing numbers with a fraction exponent, put denominator to the left of the fraction with numerator inside to the right.
NUMERATOR-power
DENOMINATOR- root

if faces with negative number and fraction exponent, take out the -1 first:
-1x49= -1xradical 49= -7

but (-49) ^1/2= -49 radical is not a real number as negative bases can only
be raised to integers (“whole numbers”)

Question 3

7.2- Negative exponents

Answer 3

negative sign on exponent= turn into a fraction (division)

ex: 5^-3 -> 1/5^3 -> 1/125

same with negative fractional exponents

Question 4

7.2- Rewriting of Fraction Exponent

Answer 4

^5radical27^4 -> 27^4/5

rules:
- x^a + x^b= x^a+b
-x^a over x^b= x^a-b
-(x^a)^b= x^axb
-x^-a= 1/x^a

when there’s fractions of variables with fractional exponents, only subtract exponents of the same variables

Question 5

7.3- multiply radicals

Answer 5

when multiplying radicals, multiply the insides as usual and simplify if necessary

if it’s a variable and number, still multiply together

if they have the same exponents, multiply insides and carry it over

if there’s a fractions of radicals and only one can be simplified, do so and leave the radical on the one that can’t

divide with exponents of a radical, leaving the remainder on the inside
**make sure to keep the power of the radical visible in your answer

Question 6

7.3 pythagorean theorem

Answer 6

formula: a^2 + b^2= c^

**make sure to look for the 90 degree and the sides connecting it are a and b
**cross out if final answer is negative as length can’t be negative

put final answer in a radical and simplify

special triangles:
-3,4,5 -6,8,10 -5,12,13

Question 7

7.4- Add and Subtract Radicals

Answer 7

**root must be dental to add/subtract, like LCD

add/subtract when finding perimeter and make sure all radicals are simplified before coming to a solution

if all can’t be added, leave it as is
ex: 22/3 + 6/2

Question 8

7.5- Multiplying

Answer 8

** do not multiply a radical with a whole number, put the whole number on the outside: /7 (3-/5)= 3/7-/35

when putting a set of parentheses to a 2nd power, WRITE IT TWICE

if powers are different when multiplying radicals, the bases must be the same and rewrite the unmatched exponents into fractions….add and put into radical
form

Question 9

7.5- Rationalizing the Denominator

Answer 9

to rationalize, ONLY multiply by the radical in the denominator, even if there is a number in the outside

Question 10

7.5- Conjugate

Answer 10

multiply by conjugate of the denominator

conjugate- change sign in the middle

**make sure to simplify radicals if possible

Question 11

7.7- Complex Numbers

Answer 11

make sure final answers are in a+bi form, with real and imaginary numbers

even with 7, 7+ 0i is possible

powers of i:
- i= /-1
- i^2= -1
-i^3= -i
-i^4= 1

conjugated i is -i

Question 12

7.7- Enhances Powers of i

Answer 12

if a exponent is a larger number, divide by 4…the remainder becomes the new exponent

***make sure to simplify to rules of i

anything to 0 power is 1 except for 0^0, which is undefined

Question 13

8.2- Quadratic Formula

Answer 13

formula: -6 +- /b^2-4(a)(c) over 2(a)

standard form: ax^2 + bx + c

to check answer, equal standard form
to 0 and factor

make sure to use i for negative radicals and reduce all outside numbers

put final answer in solution set