Arithmetic/Exponents/Exercise Answers

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Answers to Exponent Exercises

1. What are $4^{3}$ , $3^{4}$ , $1^{250}$ , ${250}^{1}?$

Answers:

a.

\ 4^{3}=4\cdot 4\cdot 4=64

b.

\ 3^{4}=3\cdot 3\cdot 3\cdot 3=81

c.

\ 1^{250}=1\cdot 1\cdot 1\cdot \ .\,.\,.\,.\ \cdot 1\cdot 1\cdot 1=1

d.

\ {250}^{1}=250

2. Write these numbers as powers of 2: $128,8,1024$

Answers:

a.

\ 128=2^{7}

b.

\ 8=2^{3}

c.

\ 1024=2^{10}

3. What is $(2^{3})*(2^{2})?$

Answer:

(2^{3})\cdot (2^{2})=2^{3+2}=2^{5}=32

4. What is $(2^{6})/(2^{2})?$

Answer:

(2^{6})/(2^{2})=2^{6-2}=2^{4}=16\

5. Harder: Why does $3^{0}=1$ ? (clue: think about ${3^{2}}/{3^{2}}$ , for example)

Answer:

{3^{2}}/{3^{2}}=3^{2-2}=3^{0}\

3^{2}=3\cdot 3=9

{3^{2}}/{3^{2}}=9/9=1\

From the first and third equations above, we can see that:

{3^{2}}/{3^{2}}=3^{0}=1\

The exponent doesn't have to be 2. The exponent can be any real number and the same logic would work. It was mentioned in the first Arithmetic chapter that a number raised to the 0 power equals 1; i. e.,

a^{0}=1\

.

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