The Laws of Exponents are composed of seven laws or rules that are applied when simplifying algebraic expressions and solving equations.

A quick review of the Product and the Quotient Law

(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 first box  to practice the Product 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 Product Law is demonstrated and the answer is shown at the bottom.
5. Practice until you understand the Product Law.
6. Click on the X when done practicing.
7. Click on the second box to practice the Quotient Law.
8. Follow the previous directions.

In your notes, complete the following two sentences.

1. The Product Law states that when multiplying exponential expressions with the same base, you should __________________.
   
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   Check Your Answer

   Add the exponents and leave the base the same.
2. The Quotient Law states that when dividing exponential expressions with the same base, you should __________________.
   
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   Subtract the exponents and leave the base the same.
3. Write an expression describing the area in square units of a rectangle with a length of 2x⁵y⁴ units and a width of 5xy units.
   
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   Check Your Answer

   The area formula of a rectangle is the length multiplied by the width. To multiply 2x⁵y⁴ by 5xy: multiply the constants then multiply like variables together by adding the exponents.

   A = 2x⁵y⁴ · 5xy = (2 · 5) (x⁵ · x)(y⁴ · y) = 10x⁶y⁵