Algebra 2 Unit 3 Review

Exponent Properties

100

3⁰+4⁰

2

200

(x³)(y¹⁰)(x⁵)(y⁶)

x⁸y¹⁶

300

(6x^-7y²x⁵)³

216x^-6y⁶

400

(2x⁵y⁶x^-3y^-3)² *(2x²)

8x⁶y⁶

500

(5^1/2*5^-3/2)^-1/4

5^1/4

nth roots and rational exponents

100

(-216)^1/3

-6

200

8^5/3

32

300

(49)^-3/2

1/343

400

(16)^1/3-5(2)^1/3

-3(2^1/3)

500

(144a²b²c⁴)^1/2

12abc²

Transformations

100

Let the graph of g be a vertical shrink by a factor of 2. f(x)=sqrt(x)

2sqrt(x)

200

Let g be a reflection in the x-axis, followed by a translation 7 units right of the graph of f(x)=sqrt(x) Write a rule for g.

-sqrt(x-7)

300

Let g be a reflection in the x-axis, followed by a translation 5 units right, 4 up of the graph of f(x)=sqrt(x) Write a rule for g.

g(x)=sqrt(x-5)+4

400

Let g be a reflection in the y-axis, no vertical stretch followed by a translation 3 units right, 2 up of the graph of f(x)=sqrt(x) Write a rule for g.

g(x)=sqrt(-x-3)+2

500

Let g be a reflection in the x-axis, followed by a translation 7 units right and vertical stretch by a factor of 4 of the graph of f(x)=sqrt(x) Write a rule for g.

-4sqrt(x-7)

Solving Radical Equations

100

2sqrt(x)=4

x=4

200

cuberoot(2x-9)=2

x=17/2

300

3sqrt(49)+x=10

x=-11

400

2cuberoot(x-2)=6

x=29

500

4sqrt(x+8)=10

x=-412/64 or x= -103/16

true or false

100

I can multiply exponent when they have the same base 

false

200

when you raise a variable to the 1/2 it is the same as finding its square root 

true 

300

Thr product porperty for radicals states you can multiply whats inside the radicand if you have the same index

true

400

If you multiply two numbers and both are raised to the same exponent, I can add the numbers

false, you multiply them 

500

If you have a horizontal stretch/shrink shift, you apply the factor as is, but with a vertical stretch/shrink you flip the factor. 

false