View source for Algebra/Further Arithmetic/Answers to Exponent Exercises 1

==== Answers to Exponent Exercises ====
1. What are <math>4^3</math>, <math>3^4</math>, <math>1^{250}</math>, <math>{250}^1?</math>

<br>'''Answers:'''

::a.  <math>\ 4^3 = 4 \cdot 4 \cdot 4 = 64 </math>

::b.  <math>\ 3^4 = 3 \cdot 3 \cdot 3 \cdot 3 = 81 </math>

::c.  <math>\ 1^{250} = 1 \cdot 1 \cdot 1 \cdot \ .\,.\,.\,.\  \cdot 1 \cdot 1 \cdot 1 = 1 </math>

::d.  <math>\ {250}^1 = 250 </math>


2. Write these numbers as powers of 2: <math>128, 8, 1024</math>

<br>'''Answers:'''

::a.  <math>\ 128 = 2^7 </math>

::b.  <math>\ 8 = 2^3 </math>

::c.  <math>\ 1024 = 2^{10} </math>


3. What is <math>(2^3)*(2^2)?</math>

<br>'''Answer:'''

:::<math>(2^3) \cdot (2^2) = 2^{3+2} = 2^5 = 32 </math>


4. What is <math>(2^6)/(2^2)?</math>

<br>'''Answer:'''

:::<math>(2^6)/(2^2) = 2^{6-2} = 2^4 = 16 \ </math>


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

<br>'''Answer:'''

:::<math>{3^2}/{3^2} = 3^{2-2} = 3^0 \ </math>

:::<math> 3^2 = 3 \cdot 3 = 9 </math>

:::<math> {3^2}/{3^2} = 9/9 = 1 \ </math>

::From the first and third equations above, we can see that: 
:::<math> {3^2}/{3^2} = 3^0 = 1 \ </math>

::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 [[Algebra/Arithmetic|Arithmetic]] chapter that a number raised to the 0 power equals 1; i. e.,&nbsp;&nbsp;&nbsp;&nbsp; 

<center><math> a^0 = 1 \ </math> .</center> 






'''Return to:''' [[../Further arithmetic/]]

[[Category:Algebra textbook pages]]