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

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- 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

- Simplify:
(-4)³

(-4) • (-4) • (-4)

12 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

- 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

- 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

- 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