### About Exponent Definition:

Whole number exponents (1 or larger) allow us to conveniently write the multiplication of the same number. For example: 4 x 4 x 4 x 4 x 4 x 4,
written using an exponent is 4^{6}. This is read as four to the sixth power and tells us that we have six factors of four or 4096.

Test Objectives

- Demonstrate the ability to identify the base and exponent in an exponential expression
- Demonstrate the ability to convert between a repeated multiplication and exponent form
- Demonstrate the ability to evaluate an exponential expression

#1:

Instructions: Identify the base and exponent in each.

a) 1^{4}

b) 2^{15}

c) 8^{7}

d) 9^{19}

e) 10^{12}

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#2:

Instructions: Write each in exponent form.

a) 2 x 2 x 2

b) 15 x 15 x 15 x 15 x 15

c) 7 x 7

d) 8 x 8 x 8 x 8 x 8 x 8

e) 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10

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#3:

Instructions: Write each as a repeated multiplication.

a) 215^{3}

b) 100^{2}

c) 9000^{5}

d) 14^{7}

e) 19^{4}

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#4:

Instructions: Evaluate each.

a) 10^{4}

b) 3^{3}

c) 9^{2}

d) 13^{2}

e) 2^{5}

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#5:

Instructions: Evaluate each.

a) 10^{15}

b) 3^{4}

c) 2^{7}

d) 15^{2}

e) 10^{6}

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Written Solutions:

#1:

Solutions:

a) 1^{4} : 1 - base, 4 - exponent

b) 2^{15} : 2 - base, 15 - exponent

c) 8^{7} : 8 - base, 7 - exponent

d) 9^{19} : 9 - base, 19 - exponent

e) 10^{12} : 10 - base, 12 - exponent

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#2:

Solutions:

a) 2 x 2 x 2 = 2^{3}

b) 15 x 15 x 15 x 15 x 15 = 15^{5}

c) 7 x 7 = 7^{2}

d) 8 x 8 x 8 x 8 x 8 x 8 = 8^{6}

e) 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 x 10 = 10^{10}

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#3:

Solutions:

a) 215^{3} = 215 x 215 x 215

b) 100^{2} = 100 x 100

c) 9000^{5} = 9000 x 9000 x 9000 x 9000 x 9000

d) 14^{7} = 14 x 14 x 14 x 14 x 14 x 14 x 14

e) 19^{4} = 19 x 19 x 19 x 19

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#4:

Solutions:

a) 10^{4} = 10,000

b) 3^{3} = 27

c) 9^{2} = 81

d) 13^{2} = 169

e) 2^{5} = 32

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#5:

Solutions:

a) 10^{15} = 1,000,000,000,000,000

b) 3^{4} = 81

c) 2^{7} = 128

d) 15^{2} = 225

e) 10^{6} = 1,000,000