Algebra/Further Arithmetic/Answers to Exponent Exercises 1

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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