Exponents, Square Roots, Cube Roots Oh My!

Exponents

100

How do you express 4x4xaxaxa

4²a³

200

Evaluate the expression -11³

-1331

300

Evaluate the expression -6(-5²+20)

30

400

Evaluate the expression 1/2(4³-6x3²)

5

500

You won a contest! You will be awarded one dollar on the first day, two dollars on the second day, and four dollars on the third day. The equation for the third day is 2^2. How many dollars will you receive on the 10th day?

You will receive $512 on the 10th day.

Square Roots

100

What is the square root of 16?

4

200

Solve -√196

-14

300

Evaluate the expression 12-8√36

-36

400

Solve the equation 4z²=144

z=6 and z=-6

500

The area of a crop circle is 45,216 square feet. What is the radius of the crop circle?

120 feet

Cube Roots

100

What is the cube root of 8?

2

200

What is the cube root of 1/64?

1/4

300

Evaluate the expression 15+3√125

30

400

Solve the equation w³-12=-76

w = -4

500

A baseball display case is a cube made of plastic. The volume of the cube is 125 in³. How many square inches of plastic are used to make the case?

150 sq. in.

Rational Numbers

100

Write 3/15 as a decimal.

0.2

200

Write 5/33 as a decimal.

0.15 (15 repeating)

300

Write the decimal 0.4444...as a fraction or mixed number

4/9

400

Write the repeating decimal -0.3565656...as a fraction or mixed number.

-353/990

500

A fun house mirror distorts the image it reflects. Objects reflected in the mirror appear 1.3(3 repeating) times taller. When a five-foot-tall person looks in the mirror, how tall does he appear?

6 and 2/3 feet tall

Irrational Numbers

100

Approximate the square root of 20 to the nearest integer and tenth.

4 and 4.5

200

Approximate the negative square root of 13 to the nearest integer and tenth.

-4 and -3.6

300

Which is greater? The square root of 26 or the cube root of 65?

Square root of 26

400

The equation d²=1.37h represents the relationship between the distance d (in nautical miles) you can see with a periscope and the height h (in feet) of the periscope above the water. About how far can you see when the periscope is 3 feet above the water?

About 2 nautical miles

500

The equation 3600b²=hw represents the relationship among the body surface area b (in square meters), height h (in centimeters), and weight w (in kilograms) of a person. To the nearest tenth, approximate the body surface area of a person who is 168 centimeters tall and weighs 60 kilograms. 

1.7m²