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## COMPETENCY #2 Laws of Exponents Scientific Notation

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**5 x 5 =**25 52 = 81 34 = 3 x 3 x 3 x 3 = 343 7 x 7 x 7 = 73 =**52 x 54**= 56 (5 x 5) (5 x 5 x 5 x 5) Do you see a pattern or shortcut?**33 x 35**= 38 (3x3x3) (3x3x3x3x3) Do you see a pattern or shortcut?**a3 x a5**= a8 (a x a x a) (a x a x a x a x a) Do you see a pattern or shortcut?**Product of Powers Property**• To multiply powers (exponents) with the same base, add their exponents. a³ x a²= a3 + 2 = a5**25**2 x 2 x 2 x 2 x 2 22 = = 23 2 x 2 x 2 1 Do you see a pattern or shortcut? 43 45 4 x 4 x 4 x 4 x 4 = = 42 4 x 4 1**Quotient of Powers Property**• To divide powers with the same base, subtract the exponent of the denominator from the exponent of the numerator. 68 = 68-5 =63 65**REVIEW**• When multiplying- add the exponents • When dividing- subtract the exponents.**EXAMPLES**b7 • b3 = b10 23 • 22 = 69 = 64 25 Z8 = z3 z5 65**Zero Exponents**• For any nonzero number a, a0 = 1 • Anything to the zero power equals 1 (except zero) 40 = 1000 = 1 1**Negative Exponents**• For any nonzero number a and any integer n, a-n = 1/an 5-2 = 1 52**1**3-5 = 3y-2 = 3 y2 35 1 5-2 = a-7b3 = b3 52 a7**5-8 + -3 =**5-11 5-8 x 5-3 = 1 or 511 a-2 + 10 = a8 a-2 x a10 =**b-8 + 5 =**b-3 b-8 x b5 = 1 or b3 3-4 + 11 = 37 3-4 x 311 =**35**1 35 - 8 3-3 = or = 38 33 a6 a8 a6 – (-2) = = a-2 m2 m2 – (-4) m6 = = m-4**Scientific Notation**• is a short hand way of writing numbers using powers of 10**Standard Product Scientific Notation Form Notation**120,000,000 1.2 x 108 1.2 x 100,000,000**Write in scientific notation.**4.62 x 109 46,200,000,000 = Where is the decimal now? Move the decimal to the right of the first significant digit.**Write in scientific notation.**8.9 x 107 89,000,000 = Where is the decimal now? Move the decimal to the right of the first significant digit.**Write in scientific notation.**3.04 x 1011 304,000,000,000 = Where is the decimal now? Move the decimal to the right of the first significant digit.**Standard Product Scientific Notation Form Notation**0.00056 5.6 x 10-4 5.6 x 0.0001**Write in scientific notation.**5.2 x 10-7 0.00000052 = # is less than 1 so exponent is negative Move the decimal to the right of the first significant digit.**Write in scientific notation.**1.06 x 10-9 0.00000000106 = # is less than 1 so exponent is negative Move the decimal to the right of the first significant digit.**Write in standard form.**3 2 0 0 0 0 0 0 3.2 x 107 = Count the # of spaces to move and fill in with zeros. Positive Exponents move the decimal to the right**Write in standard form.**6 0 4 0 0 0 6.04 x 105= Count the # of spaces to move and fill in with zeros. Positive Exponents move the decimal to the right**Write in standard form.**1.3 x 10-5= 0 0 0 0 1 3 Count the # of spaces to move left and fill in with zeros. Then add a decimal point Negative Exponents move the decimal to the left. # less than 1.**Write in standard form.**2.07 x 10-4= 0 0 0 2 0 7 Count the # of spaces to move left and fill in with zeros. Then add a decimal point Negative Exponents move the decimal to the left. # less than 1.**Write these in scientific notation.**4.1 x 103 4100 0.000067 6.7 x 10-5 62,000,000 6.2 x 107 0.000000003 3 x 10-9**Write these in standard form.**3,040 3.04 x 103 7.2 x 105 720,000 5 x 10-3 0.005 3.8 x 10-6 0.0000038