Evaluate the given expression

if a = 4 and b = –3.

a²− b³

43

Simplify using the Laws of Exponents:   

n⁷

n³

n⁴ 

Simplify using the Laws of Exponents.

−4x²y(−3xy³)

12x³ y⁴

Simplify using the Laws of Exponents.

 [(u³)²]⁴

u²⁴

Simplify using the Laws of Exponents, using only positive exponents.

 42c⁴

-6c¹²

-7

c⁸

Marta is making a quilt in the shape of a square. The length of one edge of the quilt is 2g²h³ .

What is the area of the quilt?

4g⁴ h⁶

Write 2.18 as a mixed number

in simplest form.

2 ^9/₅₀

Write 7^-5 using a positive exponent.

 1 

7⁵

Find the missing exponent in the equation:

3y⁵ · y^□ = 3y¹⁰

5

The volume of a drop of water is 0.00005 liter.

Write this number in scientific notation.

5 × 10^-5 

Write 3.07 × 10-4

in standard form.

0.000307

 Evaluate the expression.

Express the result in scientific notation.

(1.2 × 10⁴ )(3.2 × 10^-6 )

3.84 × 10^-2

The closest distance from Venus to Earth is about 40,000,000 km.  The closest distance from Saturn to Earth is about 1.2 × 10⁹ km.  

How many times closer to Earth is Venus than Saturn? 

Write your answer in standard notation. 

30

Evaluate (2.1 × 10⁴) + (5.68 × 10^-2).

Express the result in standard form. 

21,000.0568

Find ³√729 . 

9

The area of a square carpet tile is 900 cm².  

What is the length of one side of the square tile?

30 cm

Without using a calculator, which is greater,

8  or  ³√510  ?

Explain your reasoning.

Answer: 8

Reasoning: 8³ = 512 and 512 > 510

Which number(s) in the set listed below are irrational numbers?

{- ^₂/₅ , 0.005, 3.2 × 10^-4 , π, √13 } 

π, √13 

Order the set of numbers from least to greatest. 

{4.509, ²²⁹/50_, 4.09, √21}

4.09, 4.509, ²²⁹/₅₀, √21

Approximate  −√32

to the nearest integer.

− 6

What is the value of the expression (−2)⁵ ?

-32

Using exponents, what is the simplified form of

15x⁶

3x² 

5x⁴

Using exponents, what is the simplified form of

(− 2x²y)³?

−8x⁶y⁹  

Write 10^-3 using a

positive exponent.

  1  

10³

The Washington Monument weighs approximately

90,800 tons.

What is this number written in

scientific notation?

9.08 × 10⁴  

What is the value of the expression?

√¹⁹⁶/₈₁

− 14

    9

 To the nearest whole number, what is the best estimate of:

√444 ?

21

Change to a decimal:

 − 13 

  40 

− 0.325

Change to a fraction, if possible:

0.45

 5 

11

The area of a square garden is 404 sq. yards.

What is the perimeter of the garden,

to the nearest yard?

P = 80 yds

(approximately 20 yds on each side) 

Simplify.  Express the answer to the nearest integer:

  400,000,000 

  1.2 × 10⁹  

3

Natasha is seeding her backyard. The backyard is square in shape and has an area of 4,225 square feet. What is the length of one side of Natasha’s backyard?

65 ft

Name a number that is

not a

whole number.

Sample answers:

¾, −5, 35%, π, √3

Name a number that is

not an

integer.

Sample answers:

½, 47%, −1.23, π, √5

Name a number that is

not a

rational number.

Sample answers:

  π, √5

Name a number that is

not an

irrational number.

Sample answers:

¼, 0, -3, 2.5, 75%, √25

Solve the equation x² = 900.

x = ± 30

What is the value of ³√1,000? 

10

Estimate ³√30

to the nearest whole number. 

3

Simplify.

 (–5q²p)³

−125q⁶p³