1 / 12

Properties of Exponents

Properties of Exponents. Learn to apply the properties of exponents and to evaluate the zero exponent. The factors of a power, such as 7 4 , can be grouped in different ways. Notice the relationship of the exponents in each product. 7 • 7 • 7 • 7 = 7 4. (7 • 7 • 7) • 7 = 7 3 • 7 1 = 7 4.

carr
Download Presentation

Properties of Exponents

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Properties of Exponents Learn to apply the properties of exponents and to evaluate the zero exponent.

  2. The factors of a power, such as 74, can be grouped in different ways. Notice the relationship of the exponents in each product. 7 • 7 • 7 • 7 = 74 (7 • 7 • 7) • 7 = 73 • 71 = 74 (7 • 7) • (7 • 7) = 72 • 72 = 74

  3. MULTIPLYING POWERS WITH THE SAME BASE Numbers Algebra Words To multiply powers with the same base, keep the base and add the exponents. bm • bn = bm+ n 35• 38 = 35 + 8 = 313

  4. A. 66 •63 6 6 + 3 6 9 n 5 + 7 n 12 Multiplying Powers with the Same Base Multiply. Write the product as one power. Add exponents. B. n5 •n7 Add exponents.

  5. 1 Think: 2 = 2 2 5 + 1 2 6 24 4 + 4 24 8 Multiplying Powers with the Same Base Continued Multiply. Write the product as one power. C. 25• 2 Add exponents. D.244• 244 Add exponents.

  6. 5555 5 5555 5 5 5 = = = 5 •5 = 52 555 555 53 DIVIDING POWERS WITH THE SAME BASE Words Numbers Algebra To divide powers with the samebase, keep the base and subtract the exponents. 6 b 9 m = = = 6 b 6 9 – 4 m – n 5 6 b 4 n Notice what occurs when you divide powers with the same base.

  7. 5 – 3 10 – 9 x 7 9 10 3 2 5 7 x x 7 7 Think: x = x 1 Dividing Powers with the Same Base Divide. Write the quotient as one power. A. Subtract exponents. B. Subtract exponents. x

  8. 9 – 2 9 10 – 5 e 5 e Try This: Divide. Write the quotient as one power. 9 9 A. 9 2 Subtract exponents. 97 e 10 B. e 5 Subtract exponents.

  9. 4 2 = 42 – 2 = 40 = 1 1 = 2 4 1 1 (4 • 4) (4 • 4) 4 2 = 1 = = = (4 • 4) (4 • 4) 4 2 When the numerator and denominator have the same base and exponent, subtracting the exponents results in a 0 exponent. This result can be confirmed by writing out the factors.

  10. Helpful Hint 0 does not exist because 00 represents a quotient of the form But the denominator of this quotient is 0, which is impossible, since you cannot divide by 0! It is undefined! . 0n 0n 0

  11. THE ZERO POWER Algebra Words Numbers The zero power of any number except 0 equals 1. 1000 = 1 a = 1, if a 0 (–7)0 = 1

  12. 109 105 t9 t7 Practice Write the product or quotient as one power 1. n3n42. 3.4. 33 • 32 • 355. 8 • 88 = • n7 • 104 • t2 • 310 • 89

More Related