### About Exponents with Negative Bases:

In some cases, we will encounter exponential expressions where the base is negative. When this occurs, we have two different scenarios. The first is where there are parentheses around the base. The second is where there are no parentheses around the base.

Test Objectives

- Evaluate exponential expressions with a negative base enclosed in parentheses
- Evaluate exponential expressions with a negative base not enclosed in parentheses
- Demonstrate the ability to use the exponent to determine the sign of the answer

#1:

Instructions: Evaluate each.

a) (-2)^{8}

b) (-2)^{3}

c) -2^{8}

d) -2^{3}

e) (-2)^{4}

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#2:

Instructions: Evaluate each.

a) -10^{2}

b) (-10)^{2}

c) -10^{3}

d) -10^{5}

e) (-10)^{3}

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#3:

Instructions: Evaluate each.

a) (-5)^{2}

b) -5^{2}

c) (-5)^{3}

d) -5^{3}

e) (-5)^{4}

f) -5^{4}

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#4:

Instructions: Determine the sign only.

a) (-2)^{15}

b) (-8)^{12}

c) -3^{4}

d) -7^{3}

e) (-1053)^{4}

f) (-264)^{13}

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#5:

Instructions: Determine the sign only.

a) (-7)^{10}

b) (-4)^{5}

c) (-8)^{19}

d) -12^{51}

e) -1027^{16}

f) (-815)^{97}

g) (-10,577)^{113}

h) -155,375^{17}

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Written Solutions:

#1:

Solutions:

a) (-2)^{8} = 256

b) (-2)^{3} = -8

c) -2^{8} = -256

d) -2^{3} = -8

e) (-2)^{4} = 16

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#2:

Solutions:

a) -10^{2} = -100

b) (-10)^{2} = 100

c) -10^{3} = -1000

d) -10^{5} = -100,000

e) (-10)^{3} = -1000

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#3:

Solutions:

a) (-5)^{2} = 25

b) -5^{2} = -25

c) (-5)^{3} = -125

d) -5^{3} = -125

e) (-5)^{4} = 625

f) -5^{4} = -625

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#4:

Solutions:

a) (-2)^{15} : sign is negative

b) (-8)^{12} : sign is positive

c) -3^{4} : sign is negative

d) -7^{3} : sign is negative

e) (-1053)^{4} : sign is positive

f) (-264)^{13} : sign is negative

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#5:

Solutions:

a) (-7)^{10} : sign is positive

b) (-4)^{5} : sign is negative

c) (-8)^{19} : sign is negative

d) -12^{51} : sign is negative

e) -1027^{16} : sign is negative

f) (-815)^{97} : sign is negative

g) (-10,577)^{113} : sign is negative

h) -155,375^{17} : sign is negative