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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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example 1
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
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
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
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
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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