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Properties of Exponents III

Properties of Exponents III. Power to a Power Zero Power. Exponential Notation. Exponential Notation is nothing more than a shorthand notation. Instead of writing out a number or variable times itself many, many times, we use exponential notation.

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Properties of Exponents III

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  1. Properties of Exponents III Power to a Power Zero Power

  2. Exponential Notation • Exponential Notation is nothing more than a shorthand notation. Instead of writing out a number or variable times itself many, many times, we use exponential notation. • The exponent tells us how many times the base is multiplied by itself.

  3. Exponential Notation • Refer to your class notes for examples given in class.

  4. Products of Monomials • Remember, “monomial” = “one term” • Monomials are products of numbers and variables. • Refer to your class notes for examples and non-examples of monomials.

  5. Products of Monomials • This comes back to exponential notation. • Suppose we are multiplying the following monomials: • (3x4y5)(-5x3y6) • Well, according to exponential notation this is really: • (3xxxxyyyyy)(-5xxxyyyyyy) • All total there are 7 x’s and 11 y’s.

  6. Products of Monomials • Remember, we are multiplying, so -3 x 5 = -15. • Therefore, the final answer is -15x7y11. • Bottom line is, when you multiply two monomials you add the exponents! • The reason for this is because with exponential notation, we just have to remind ourselves that x4 means there are 4 x’s in the product and x3 means there are 3 more x’s to join them, making 7 total.

  7. Products of Monomials • Refer to your notes for examples from class.

  8. Quotient of Monomials • Again, we can make use of exponential notation. • Bottom line here is, we end up subtracting the exponents and leave the variable wherever the exponent was greater. • Refer to your class notes for examples.

  9. Negative Exponents • Negative exponents move the base from one part of the fraction to the other. When this occurs, the exponent becomes positive. • Remember to simplify the base before you move it. • Refer to your class notes for more examples.

  10. Power to a Power • Here again, we are going to make use of exponential notation • Remember than x5 means that we are going to multiply x by itself 5 times. • Well than (2x)5 means that we will be multiplying 2x by itself 5 times. Remember, the exponents reminds us how many times the base is being multiplied by itself. • That means we will have: (2x)(2x)(2x)(2x)(2x) = 32x5 • Likewise, (3x2y3)3 means we will multiply 3x2y3 by itself 3 times. Every factor will have a 3, 2 x’s, and 3 y’s. So: (3x2y3)(3x2y3)(3x2y3) = 27x6y9

  11. Power to a Power • Point is, when you raise a monomial to a power, you multiply the exponents of the base times the power of the monomial. • See your notes for examples from class.

  12. Zero Power • Any base raised to the power of 0 is equal to 1. • a0=1

  13. Properties of Exponents • a x a x a x … x a = an • a-n= 1/an • amx an= am+n • am/ an= am-n • (am)n= amn • a0 = 1 • (ab)n = anbn • (a/b)n = an/bn • These same properties can be found on Pages: 141, 152, 155, 331-332

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