Investigation: Properties of Exponents



Investigation: Properties of Exponents

Part 1: Rewrite the mathematical expressions.

a) 43= b) x5= c) 71=

Part 2: Use expanded form to review and generalize the properties of exponents.

Step 1 Write each product in expanded form, then write it in exponential form.

a. [pic] b. [pic] c. [pic]

Step 2 Generalize your results from Step 1. (Product Property of Exponents)

[pic]

In other words, when multiplying with the same base, you _____________ the exponents.

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Step 3 Write the numerator and denominator of each quotient in expanded form. Reduce by eliminated common factors, and then rewrite the factors that remain in exponential form.

a. [pic] b. [pic] c. [pic]

Step 4 Generalize your results from Step 3. (Quotient Property of Exponents)

[pic]

In other words, when dividing with the same base, you ______________ the exponents.

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Step 5 Write each quotient in expanded form, reduce, and rewrite in exponential form.

a. [pic] b. [pic] c. [pic]

Step 6 Now use the property you discovered in Step 4 to simplify the expressions.

a. [pic] b. [pic] c. [pic]

Step 7 Generalize your results from Steps 5 and 6. (Definition of Negative Exponents)

[pic] [pic] [pic]

In other words, a negative exponents ______________________ the base.

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Step 8 Expand each expression, and then rewrite in exponential form.

a. [pic] b. [pic] c. [pic]

Step 9 Generalize your results from Step 8. (Power of a Power Property)

[pic]

In other words, when raising an exponent to an exponent, you ____________ the exponents.

Step 10 Expand each expression, and then rewrite in exponential form. Do not multiply within the parentheses.

a. [pic] b. [pic] c. [pic]

Step 11 Generalize your results from Step 10. (Power of a Product Property)

[pic]

In other words, when monomials are being multiplied and raised to a power, you ______________ the power to the exponents.

Step 11b Is (x + 3)2 = x2 + 32? Explain.

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Step 12 Use the properties that you have discovered to simplify each expression.

a. [pic] b. [pic] c. [pic] d. [pic]

Step 13 Generalize your results from Step 12. (Zero Exponents)

[pic]

In other words, anything raised to the power of 0 is always ______________.

Practice

Rewrite each of the following expressions as a fraction or an integer without exponents.

1) 5-6 2) -26 3) (-4)2 4) -3-2

5) (-5)-4 6) (3/7)2 7) (1/2)-7 8) (2/4)-1

Simplify the following problems using the properties of exponents.

9) m4 2m-3 10) 4r-3 2r-2 11) 2k4 4k

12) 2x3 y-3 2x-1 y3 13) 2y2 3x 14) (x2)0

14) (4r0)4 15) (3k)4 16)[pic]

17) [pic] 18) [pic] 19) (y6x-2)4

20)(p4)2 2p-1 21) (2j 4f)4 22) (n2)-10 5x3

Properties of Exponents Practice Worksheet

1) 2) 3) 4)

5) 6) 7) 8)

9) 10) 11) 12)

13) 14) 15) 16)

17) 18) 19)

20) 21) 22)

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