Advanced Worksheet 4.2

Find the greatest common factor of the numbers.

  1. 220, 330
/
  1. 115, 138
/
  1. 345, 522

Find the greatest common factor of the monomials.

  1. ,
/ /

Find the greatest common factor of the monomials.

  1. Joe works in the warehouse for a company that produces light bulbs. His boss pulled out 64 cases of 60-watt bulbs, 48 cases of 75-watt bulbs, and 56 cases of 100-watt bulbs. She left instructions to package identical orders of cases of bulbs, but didn’t specify how many orders to make. Joe decided to pack the greatest possible number of orders, so that if the number was wrong, he could combine his orders into the correct number of orders. How many orders did Joe pack? Did his thinking make sense? Explain your reasoning.
  1. The greatest common factor of two numbers is 27. A factor of the first number is 8. Could the second number be 54? Explain your reasoning.

Advanced Worksheet 4.4

Find the least common multiple of the numbers.

  1. 24, 28
/
  1. 15, 35, 70
/
  1. 20, 45, 50

Find the least common multiple of the monomials.

  1. You and a friend are making bracelets. You can finish one bracelet in 180 seconds. Your friend can finish one bracelet in 210 seconds. You start making bracelets at the same time. When will be the next time you and your friend start a bracelet at the same time? Write your answer in minutes and seconds. How many bracelets have you each completed at this time?

Rewrite the variable expressions with a common denominator.

  1. ,
/
  1. ,
/
  1. ,

Advanced Worksheet 4.5

Find the product or quotient. Write your answer using exponents.

Simplify.

Find the area of the right triangle, rectangle or square.

  1. An earthquake of magnitude 6.7 releases times more energy than an earthquake of magnitude 4.7. An earthquake of magnitude 4.7 releases times more energy than an earthquake of magnitude 2.7. How many times more energy does an earthquake of magnitude 6.7 release than an earthquake of magnitude 2.7? Write your answer using an exponent.

Simplify.

Advanced Worksheet 4.6

  1. Which expression is not equivalent to ?

Write the expression using only positive exponents.

Write the expression without using a fraction bar.

Find the product. Write your answer using only positive exponents.

  1. The diameter of an atom is about centimeter. The diameter of the nucleus of the atom is about centimeter. Use the quotient of powers property to find about how many times smaller the diameter of the nucleus is than the diameter of the atom.

Find the quotient. Write your answer using only positive exponents.

Use a calculator to evaluate the expression. If necessary, round the result to the nearest thousandth.

Exponent Rules Worksheet

Simplify the expression. Write your answer using positive exponents.

Advanced Worksheet 4.7

Write the number in scientific notation.

Write the number in standard form.

Complete the statement using <, >, or =.

Find the product. Write your answer in scientific notation.

Order the numbers from least to greatest.

Write the number in scientific notation.

  1. Volume (in cubic kilometers) of water in Lake Superior: 12,100
  2. Approximate density (in grams per milliliter) of one nitrogen atom: 0.001251

Write the number in standard form.

  1. Floor area (in square meters) of the John Hancock Center in Chicago:
  2. Approximate thickness (in meters) of a United States dollar bill:
  1. The energy corresponding to the mass of an electron is given by the equation . In this equation, is the speed of light, meters per second. The mass of an electron is kilograms. Calculate the energy corresponding to the mass of one electron.