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

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?

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)

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

### 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?

• 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