This section reviews the power laws, the Power of a Power, the Power of a Product Law, and the Power of a Quotient Law. Experiment with the power laws below.

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(After clicking on the link above, follow the directions below.)

  1. Click on “Bigger” in the upper right hand corner.
    (The following images are only illustrations. Follow the link above to complete the activity.)
  2. Click on the third box  to practice the Power of a Power Law.
  3. The m-value (purple), n-value (orange), and x-variable are changed by moving your cursor to the left or right on the purple, orange or red number line.
  4. Select different values for m-, n-, and  x–values. Each time a new value is selected, the Law is demonstrated and the answer is shown at the bottom.
  5. Practice until you understand the Power of a Power Law.
  6. Click on the X when done practicing.
  7. Click on the fourth box to practice the Power of a Product Law.
  8. Follow the previous directions.
  9. Many students get confused about the difference between the Power of a Power Law and the Power of a Product Law. Make sure that you can tell the differences between the two.
  10. Click on the fifth box to practice the Quotient of a Product Law.
  11. Follow the previous directions.

Note: The Power of a Product Law and the Power of a Quotient Law only have one exponent.

In your notes, complete the following sentences and solve the problem:

  1. The Power of a Power Law states that when taking an exponential expression to a power, you should __________________.

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    Check Your Answer

    Leave the bases the same and multiply the exponents. Close Pop Up
  2. The Power of a Product Law states that when multiplying exponential expressions with the same base you should __________________.

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    Check Your Answer

    Leave the base the same and add the exponents. Close Pop Up
  3. The Power of a Quotient Law states that when dividing exponential expressions with the same base, you should __________________.

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    Check Your Answer

    Leave the base the same and subtract the exponents. Close Pop Up
  4. The side of a square is 6x3y2 feet. Find the area of the square. Hint: Use A = s2 for the formula.

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    Check Your Answer

    A = (6x3y2)2 = (6)2(x3)2(y2)2 = 36x6y4 sq ftClose Pop Up