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Multiplying numbers w/exponents Absent Copy 11/6,7. Example 1. Write in exponential form: 2 • 2 • 2 • 2 • 2 2 ? there are 5 two’s 2 5 Solution. What does exponential form mean? It means to write the problem using the base and a exponent. Which number is base?

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## Multiplying numbers w/exponents Absent Copy 11/6,7

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**Example 1**• Write in exponential form: 2 • 2 • 2 • 2 • 2 2? there are 5 two’s 25 Solution • What does exponential form mean? • It means to write the problem using the base and a exponent. • Which number is base? • 2 is the factor which is also the base • How many 2 do we have? • We have 5 two’s. • So what do you think the exponent will be? • The exponent will be 5 • What do we do last? • Re- write the problem in exponential form. 25**Example 2**• Simplify: (-4)³ (-4) • (-4) • (-4) 1 2 3 (-4) • (-4) • (-4) = -64 Solution • Which number is the base? • The factor (-4) is the base • Which number is the exponent? • 3 is the exponent • What do we do first? • We write out the factor (-4) three times • How many neg. signs do we have? • We have 3 neg. signs. • Odd # of neg. signs the answer is Negative. • What do we do next? • Multiply the factor (-4) three times -64**Example 3**• Simplify: 34 3 • 3 • 3 •3 1 2 3 4 3 • 3 • 3 •3 = 81 Solution • Which number is the base? • 3 is the base • Which number is the exponent? • 4 is the exponent • What do we do first? • Write out the factor (3) four times. • What do we do next? • Multiply all the factor’s (3) together 81**Example 4**• Simplify the expression for the given values of the variable: • p³ - 6 for p = -3 (-3)3+-6 (-3) • (-3) • (-3) 1 2 3 (-3)• (-3) • (-3) = -27 -27 + -6 = -33 Solution • What is the first step in simplifying this expression? • Change the sub. Sign. Add the opp. • Re-write problem substituting the value of the variable (-3) • What do we do next? • Write out the factor (-3) three times • How many neg. signs do we have? • We have 3 neg. signs. • Odd # of neg. signs then the multiplication part of problem is neg. • What do we do next? • Follow GEMA • Multiply the factor (-3) three times and re-write the problem. • What integer rule do we use last? • Same signs add the #’s and keep the sign they both have. -33**Example 5**• Simplify the expression for the given values of the variable: xp + f2forx = -4, p = 2, f = 5 (-4)2+ (5)2 (-4) • (-4) + (5)• (5) 1 2 (-4) • (-4) = 16 (5) • (5) = 25 16 + 25 = 41 Solution • What is the first step in simplifying this expression? • Re-write problem substituting the values for all the variables. • What do we do next? • Write out all the factors (bases) twice. • How many neg. signs do we have with (-4) base? • We have 2 neg. signs • Even number of neg. signs means multiplication problem is positive. • What do we do next? • Multiply each factor (base) twice • What integer rule do we use when adding 2 #’s? • Same signs you add the #’s and keep the sign they both have. 41

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