Exponents and Scientific Notation

Monomials

100

Is 87 a monomial? Why or why not?

Yes because it is a number.

200

Is 4x⁹ a monomial? Why or why not?

Yes because it is a number multiplied by a variable.

300

Is 5a⁵b⁷ a monomial?  Why or why not?

Yes because it is a number multiplied by variables.

400

Is (27x³)/(32) a monomial?  Why or why not?

Yes because it is a variable (x³) multiplied by a number (27/32).

500

Is (46a²)/(9b) a monomial?  Why or why not?

No because there is a variable in the denominator.

Simplifying

100

Simplify:

x^-5x⁸

x³

200

Simplify:

4^-3

1/64

300

Simplify:

b⁴b^-7

1/b³

400

Simplify:

((2x²y⁶)⁵)⁰(3x²y³)⁴

81x⁸y¹²

500

Simplify:

(3⁶x⁴y^-3)/(3³x^-3y²)

(27x⁷)/(y⁵)

Area and Volume

100

A rectangle has a width of 4xy³ and a length of 5x²y².  What is the area?

20x³y⁵

200

A triangle has a base of 4a³b and a height of 8a⁵b⁷.  What is the area?

16a⁸b⁸

300

A cube has a length of 5x⁴.  What is the volume?

125x¹²

400

A circle has a radius of 6a³.  What is the area?

36a⁶ pi

500

A block has a width of mn⁴, a length of 2m²n, and a height of 3n⁵.  What is the volume?

6m³n¹⁰

Scientific Notation

100

Write in scientific notation:

2,900,000

2.9*10⁶

200

Write in standard form:

2.05*10^-5

0.0000205

300

Evaluate. Write in both scientific notation and standard form:

(5.3*10⁵)(2*10⁴)

scientific notation: 1.06*10¹⁰

standard form: 10,600,000,000

400

Evaluate.  Write in both scientific notation and standard form:

(4.2*10^-3)²

scientific notation: 1.764*10^-5

standard form: 0.00001764

500

Evaluate.  Write in both scientific notation and standard form:

(3.6*10⁴)/(4*10^-3)

scientific notation: 9*10⁷

standard form: 90,000,000

Word Problems

100

A cube has a side length of 3*10⁶ inches.  What is the volume?

2.7*10¹⁹ inches³

200

Kasey spends $2.3*10³ a month.  There are 1.2*10 months in a year.  How much money does Kasey spend each year.

Kasey spends $27,600 each year. (2.76*10⁴)

300

A corporation earned a profit of $2.5*10⁴ for 1*10³ days on a row.  What was the corporation's total profit during this time period?

The corporation's total profit was $25,000,000. (2.5*10⁷)

400

Dunkin Donut's parking lot is 1.6*10⁵ square feet.  Starbucks' parking lot is 3.2*10⁵ square feet.  How many times bigger is Starbucks' parking lot compared to Dunkin's?

Starbucks' parking lot is two times bigger than Dunkin's.

500

The population of Montville is 4*10⁶ and the population of Lincoln Park is 8*10³.  How many times the population of Lincoln Park is Montville?

Montville has 500 times the population of Lincoln Park. (5*10²)