Algebra 2

Rational Exponents

100

What is X to the power of 8/9

⁹√x⁸

200

What is M to the power of 3/4

⁴√m³

300

What is T to the power of 11/13

¹³√t¹¹

400

What is P to the power of 103/124

¹²⁴√p¹⁰³

500

What is y to the power of 4234/6493

⁶⁴⁹³√y⁴²³⁴

Prop. of Rat. Ex

100

What is x^4/6 divided by x^2/6

⁶√x²

This is because you have to subtract the numerators then take the denominator and square it on the outside and take the square root of x to the power of the numerator.

200

What is v^6/8 divided by v^1/4

⁸√v³

300

What is x^8/10 divided by x^4/10

¹⁰√x⁴

400

what is c^15/30 divided by x^5/30

³⁰√c¹⁰

500

what is b^45/80 divided by b^16/80

⁸⁰√b²⁹

Complex Numbers

100

What is √-36

6i

Because you rewrite it as √-36 √-1 times √36

This means √-1 is an imaginary number and simplifies √-36 to 6i

200

What is √-49

7i

300

What is √-45

6.7i

400

what is √-16

4i

500

What category is i⁴³

This would be -i because you divide the exponent by 4 and if their is a remainder of 1 it is i, if its 2 then it is -1, if its 3 then its -i and if there is no remainder it is 1

Polynomials

100

what is the right way to write x-35x⁴+15x²-2x³+ 

-35x⁴-2x³+15x²+x, this is because the highest power goes first

200

Place the following in descending order 10x²-4-5x⁴-4x-9x³

-5x⁴-9x³+10x²-4x-4

300

Place the number in ascending order 6v+8v⁴-2v²+7v³

6v-2v²+7v³+8v⁴

400

Place the following in descending order 10b-11b⁶-4b²-5b⁴

-11b⁶-5b⁴-4b²+10b

500

Place the following in ascending order 33b-2b²-9b⁴-7b³+b⁵

33b-2b²-7b³-9b⁴+b⁵

Ope. of Comp. Num.

100

i√15 ^. i√5

i²√75, this is because you multiple the two number together inside the square root.

200

i√10 ^. i√10

i²√100

300

i√8 ^. i√9

i²√72

400

What is 10/2i

10i/-2, you want the imaginary number as the numerator so you take 10/2i and multiply them both by i and get 10i/2i² and i² is also -1 so you have 10i/-2

500

what is 7/4i

7i/-4