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How Do You Solve a Word Problem by Taking a Monomial to a Power?

Find the volume of a cube box whose sides have the length 2a2b. Write the solution as a monomial in simplest form.

Summary

  1. The cube's sides have the length '2a2b'
  2. A cube, by definition, has sides of equal lengths
  3. 'a' and 'b' are variables
  4. The volume of a cube is the 'cube' of one of it's lengths
  5. The 'cube of something' is just a fancy way of saying 'something to the 3rd power'
  6. We use the power of a product rule to distribute the exponent '3' to each factor in '2a2b'
  7. (a2)3 = a2 • 3 = a6
  8. 23 = 8

Notes

    1. A cube, by definition, has sides of equal lengths
    1. 'a' and 'b' are variables
    1. We use the power of a product rule to distribute the exponent '3' to each factor in '2a2b'
    2. 'a' and 'b' are variables
    1. 'a' is a variable
    1. 'a' and 'b' are variables
    1. '23' = 2 • 2 • 2 = 8
    1. 'a' and 'b' are variables