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Simplify the Expression

100

z⁶ * z⁴

z¹⁰

200

(x⁴)^-7 

1 / x²⁸

300

(x^-2 * x⁹)^-3

1 / x²¹

400

(x^-2 * y⁰) / (x⁴ * y^-5)

y⁵ / x⁶

500

( 7x⁵ / 4y³)²

49x¹⁰ / 16y⁶

Evaluate the Expression

100

The 4th root of 625

5

200

The third root of -27

-3

300

36^3/2

216

400

27^2/3

9

500

(1/64)^-1/3

4

Growth and Decay

100

x:  0  1  2  3

y:  1  4  7  10

Growth, Decay, or neither?

Neither

200

x:   1    3    5   7

y: 108  36  12  4

Growth, Decay, or neither?

Decay

300

A city has a population of 775,000. The population y increases by 3% each year.

Write an exponential function that represents the population after t years.

775,000(1.03)^t

400

A website has 400,000 members. The number y of members increases by 6% each year.

Write an exponential function that represents the website membership after t years.

400,000(1.06)^t

500

The value of a car is $22,500. It loses 11% of its value every year. 

Estimate the value of the car after 5 years.

$12,564.13

Exponential Equations

100

2^x = 2¹⁹

x = 19

200

25^x = 5^x-5

x = -5

300

343^1/2 = 7^x+1/2

x = 1

400

1/8 = 2^2x-1

x = -1

500

(1/4)^5x = 32^2x+8

x = -2

Geometric Sequence

100

768, 192, 48, 12, 3, 0.75, ...

Geometric, Arithmetic, or neither

Geometric

200

1, -2, 4, -7, 10 ...

Geometric, Arithmetic, or neither

neither

300

Write the next three terms of the geometric sequence. 

-6, 12, -24, 48, ...

-96, 192, -384

400

Write an equation for the nth term of the geometric sequence

448, −112, 28, −7, …

a_n = 448(-1/4)^n-1

500

Find the 17th term in the sequence

30, 120, 480, 1920, .

128,849,018,880