Exponents, Radicals, & Geometric Sequences

Exponents A

100

(2x²y)³(-3xy³)²

72x⁸y⁹

200

Simplify and write without negative powers

-2ab(5b²c)³

-250ab⁷c³

300

Simplify and write without negative powers

(4x/y³)^-2

y⁶/16x²

400

(5x/y)² (y³/10x²)

5y/2

500

Simplify and write without negative powers

(3xy^-2)²(2x³yz)(6yz²)^-1

3x⁵/y⁴z

Exponents B

100

Simplify and write without any negative powers (-5x²y^-1)⁴

625x⁸/y⁴

200

Simplify and write without any negative powers 

[(c²d^-2)/c]⁵

c⁵/d¹⁰

300

Simplify and write without any negative powers 

(x²y²z^-1)³(xyz⁴)(x³y)

x¹⁰y⁸z

400

Simplify and write without any negative powers (m²n^-5)⁰(m^-7)

1/m⁷

500

Simplify and write without any negative powers 

[(2x^-2)/3] (3x/4)²

3/8

Geometric Sequence

100

What is the next 3 terms of the geometric sequence?2, 6, 18, 54,...

162, 486, 1458

(r=3)

200

Write the recursive formula for the following sequence:

1, 3, 9, 27, 81, ...

a₁=1

a_n= 3 a_n-1

300

What is the recursive formula for the following sequence:

64, -16, 4, -1, ...

a₁=64

a_n=(-1/4) a_n-1

400

Write the explicit formula for the following geometric sequence:

1, 5, 25, ...

a_n=1(5)^n-1

500

Find the eighth term of the sequence

4,16, 64, 256, ...

a_n=4(4)^n-1; 65,536

Arithmetic Sequence

100

What are the next three terms for the arithmetic sequence 

-6, -10, -14, ...

-18, -22, -26

200

Find the common difference of the following arithmetic sequence:

-8, -13, -18, -23, ...

d=-5

300

determine the common difference of the following arithmetic sequence:

-2.3, -1.1, 0.1, 1.3, ...

d= 1.2

400

Determine the explicit formula for the following sequence:

3, -3, -9, -15,... 

a_n=3- 6(n-1) = -6n+9

500

What is the 20th term of the following arithmetic sequence:

7, 4, 1, ...

-50 

Radicals

100

Write the following expression in the simplest radical form

√ (40)

2 √ (10)

200

Simplify the expression

√ (4m⁷)

2m³ √ (m)

300

Write in the simplest radical form

4√ (27) + 6√ (12)

24 √ (3)

400

Write the expression in the simplest form

3√(32)/ √(2)

12

500

Write the expression in simplest form. 

√(x²y²)/ √(y)

xy²