Exponents, Radicals, and Exponential Functions

Exponents

100

(2x^3y^4)(2x^4y^3)

4x^7y^7

200

(-3x^2y^4)^3

-27x^6y^12

300

(x^12y^7)/(x^4y^12)

x^8/y^5

400

(2x^5y^-3)^-2

y^6/(4x^10)

500

(5x^3(5y^3)^2)/(5^3x^8y^7(2xz)^-2

(4z^2)/(x^3y)

Rational Exponents

100

Convert to radical form:

a^(2/3)

root3(a)^2

200

Convert to radical form :

sqrt(5x)

300

Convert to radical form:

root4(15)^3

15^(3/4)

400

Convert to radical form and simplify:

16^(3/2)

64

500

Convert to radical form and simplify:

125^(4/3)

625

Radicals

100

Simplify:

sqrt(80

4sqrt(5)

200

sqrt(120)

2sqrt(30)

300

sqrt(36x^2

6x

400

5^(3/2)

(sqrt5)^3

500

root3(16x^4y^7

2xy^2root3(2xy)

Geometric Sequences

100

Is this Geometric? 

-3, 6, -9, 12

No 

200

Is this Geometric? If so - what is the common ratio?

7, 21, 63, 189

Yes, r = 3

300

Find the 8th term:

.25, .50, 1...

32

400

Find the 7th term

-4, 12, -36..

-2916

500

Find the 7th term:

36, 6, 1/6....HINT (answer needs to be in fraction form)

1/1296

Growth and Decay

100

Will this graph show growth or decay:

y=2(3)^x

Growth

200

The population of bugs is currently 1800. They decrease at a constant rate of 4%. After 7 years, what will the bug population be?

1253 bugs

300

The half life of Unicorn blood is 8 hours.  If you start with 100 grams, how much will be viable after one day?

12.5 grams

400

What do you get as your y value if you plug x=-3 into the exponential function below:

y=2(.25)^x

128

500

You invest $14,000 in a savings account that is compounded quarterly at a rate of 2%. After 9 years, how much will be in the account?

$16,753.53