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Worksheet: Applications of Powers and Exponents

Q1:

There are nearly 3 5 species of monkeys on Earth. What is the value of 3 5 ?

Q2:

The sun is about 10 10 10 10 10 10 10 1 0 m i l e s away from the earth. Write the distance in exponential form and then evaluate it, giving your answer in millions of miles.

  • A 8 1 0 , 10.74 million miles
  • B 1 0 7 , 10 million miles
  • C 1 0 8 , 10 million miles
  • D 1 0 8 , 100 million miles
  • E 1 0 9 , 1 0 0 0 million miles

Q3:

Anthony scored 2 7 points in a board game, and Noah scored 7 2 points. Determine who won the game and by how many points.

  • AAnthony, 177 points
  • BNoah, 79 points
  • CNoah, 177 points
  • DAnthony, 79 points
  • EAnthony, 128 points

Q4:

The amount of wax this candle mold can hold is measured in cubic units. Find how much wax it can hold by using the expression 𝑠 × 𝑠 × 𝑠 , where 𝑠 is the length of a side.

  • A56
  • B42
  • C 8 232
  • D 2 744
  • E84

Q5:

A football stadium has 1 6 4 seats, and a cricket stadium has 5 7 seats. Which stadium has more seats? How many more?

  • A the cricket stadium, 4 8 7 2 9
  • B the football stadium, 1 2 5 8 9
  • C the cricket stadium, 2 1 5 8 9
  • D the cricket stadium, 1 2 5 8 9
  • E the cricket stadium, 6 5 5 3 6

Q6:

The area of San Bernardino County in California is about 3 9 square miles. Write this as a product and then evaluate it to find the area.

  • A 9 3 = 2 7 square miles
  • B 9 9 9 = 7 2 9 square miles
  • C 3 3 3 3 3 3 3 3 = 6 5 6 1 square miles
  • D 3 3 3 3 3 3 3 3 3 = 1 9 6 8 3 square miles
  • E 9 3 3 = 8 1 square miles

Q7:

There were 2 8 ants in a nest. After the eggs hatched, the number of ants was 2 5 times more than before. How many ants are there now? Leave your answer in exponential form.

  • A 2 3
  • B 4 1 3
  • C 2 4 0
  • D 2 1 3
  • E 4 4 0

Q8:

Which of the following is true?

  • A ( 2 2 ) 2 5
  • B ( 2 2 ) 2 5

Q9:

If four times a number is 4 3 , find 7 4 times this number.

Q10:

In the year 2000, the governor of Washington, Gary Locke, received about 1 0 6 votes to win the election. Write this as a product and state the number of votes received.

  • A 6 × 1 0 , 60 votes
  • B 6 × 6 × 6 × 6 × 6 × 6 × 6 × 6 × 6 × 6 , 6 0 4 6 6 1 7 6 votes
  • C 1 0 × 1 0 × 1 0 × 1 0 × 1 0 × 1 0 , 6 0 0 0 0 0 0 votes
  • D 1 0 × 1 0 × 1 0 × 1 0 × 1 0 × 1 0 , 1 0 0 0 0 0 0 votes
  • E 6 × 1 0 × 1 0 × 1 0 × 1 0 × 1 0 × 1 0 , 6 0 0 0 0 0 0 votes

Q11:

Without evaluating the powers, order 2 5 , 2 4 , and 2 3 from least to greatest.

  • A 2 , 2 , 2 3 5 4
  • B 2 , 2 , 2 5 4 3
  • C 2 , 2 , 2 5 3 4
  • D 2 , 2 , 2 3 4 5
  • E 2 , 2 , 2 4 3 5

Q12:

Order the following numbers from least to greatest: 1 4 , 3 , 1 6 , 1 5 4 5 7 .

  • A 1 , 3 , 1 6 , 1 4 7 4 5 5
  • B 1 6 , 1 4 , 3 , 1 5 5 4 7
  • C 1 6 , 1 4 , 1 , 3 5 5 7 4
  • D 1 , 3 , 1 4 , 1 6 7 4 5 5
  • E 3 , 1 6 , 1 4 , 1 4 5 5 7

Q13:

A festival was expected to have 3 1 1 people. One week before the festival, it was discovered that the number of people expected to attend had tripled. How many people are expected to attend? Write your answer in the form 𝑎 𝑏 .

  • A 3 1 0
  • B 3 2 2
  • C 3 1 4
  • D 3 1 2
  • E 3 1 1

Q14:

The prefix giga in gigameter represents 1 0 0 0 0 0 0 0 0 0 meters. Express this as a power of ten.

  • A 1 0 1 2 meters
  • B 1 0 6 meters
  • C 1 0 3 meters
  • D 1 0 9 meters
  • E 1 0 8 meters

Q15:

Order the following from least to greatest: .

  • A
  • B
  • C
  • D
  • E

Q16:

If a library has 9 4 books, how many books are there?

  • A94 books
  • B 262 144 books
  • C49 books
  • D 6 561 books
  • E36 books

Q17:

Which of the following is true?

  • A | 3 0 | > 8 2
  • B | 3 0 | = 8 2
  • C | 3 0 | < 8 2

Q18:

The number of calories in one croissant can be expressed as 6 3 . Determine the whole number that represents 6 3 .

Q19:

Which of the following is true?

  • A 1 1 2 × 1 2 = 1 2 4 3
  • B 1 1 2 × 1 2 > 1 2 4 3
  • C 1 1 2 × 1 2 < 1 2 4 3

Q20:

Order the following from greatest to least: .

  • A
  • B
  • C
  • D

Q21:

Select the pair of powers which have the same value.

  • A 6 2 and 8 2
  • B 6 2 and 2 8
  • C 2 6 and 2 8
  • D 2 6 and 8 2
  • E 2 7 and 8 3

Q22:

If Charlotte zooms out three times on an interactive map, the scale is 1 0 3 times greater. Write this number in standard form.

Q23:

There are 100 or 1 0 2 pennies in each dollar. Using exponents, determine how many pennies there are in $100.

  • A 1 0 2
  • B10
  • C 1 0 3
  • D 1 0 4

Q24:

The length of one sidereal day on Venus is 3 5 Earth days. Express this as a product and then evaluate it to find the number of Earth days in one sidereal Venus day.

  • A 5 3 = 1 5 Earth days
  • B 5 5 5 = 1 2 5 Earth days
  • C 5 5 = 2 5 Earth days
  • D 3 3 3 3 3 = 2 4 3 Earth days
  • E 5 5 5 5 5 = 3 1 2 5 Earth days

Q25:

A 100-pound person on Earth would weigh about 𝑥 pounds on Jupiter. If 𝑥 is equal to 4 4 4 4 , write 𝑥 in exponential form and evaluate the exponent.

  • A 2 4 , 16
  • B 4 4 , 16
  • C 4 8 , 256
  • D 4 4 , 256
  • E 4 1 6 , 64