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{\large {\bf   1.08 Exponents Tuesday Homework }}
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     For any number $x$  \hspace{40pt} $x^2 = x \cdot x$ \hspace{40pt} $x^3 = x \cdot x \cdot x$ \hspace{40pt} $x^4 = x \cdot x \cdot x \cdot x$
 
  $x^1 = x  $ \hspace{40pt} $x^0 = 1  $ \hspace{40pt} $x^{-1} = \frac{1}{x}$\hspace{40pt}$x^{-2} = \frac{1}{x^2}$
  
  
 (1) Calculate all of these quantities for $x =2$. Thus, your first two answers will be  $2^2 = 4$ and  $2^3 =8. $
 
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  (2) Calculate all of these quantities for $x=3$. 
  
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  (3) Calculate all of these quantities for $x =5$. 
  
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  (4) Calculate all  of these quantities for $x=10$. 
  
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  (5) In your answer to (4), what do you notice about the zeroes? 
  
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  (6) What is $3^2 + 3^1$?  \hspace{80pt}  (7) What is $3^2 \cdot 3^1$?  
  
  
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  Answers: (8)   $z = 3$.  (9) $2^2  \cdot 2^4 = 4 \cdot 16 = 64 = 2^6$. (10) $10^4 \cdot  10^8 = 10^{12} = 1,000,000,000,000. $ (11) $10^1 \cdot 10^1 =    10^2 = 100$. 
 (12)  $10^0 \cdot 10^1 = 10^1 = 10$. 
 (13)   $10^3 \cdot 10^{-1}  = 10^2 = 100$. 
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  (8) Your answer to question (7) should be $3^z$, where $z$ is some number. What is $z$? 
  
     For any numbers $x,a,$  and $b$,  \hspace{40pt} $x^a \cdot x^b = x^{a+b}$.
     
 
   
   (9) What is $2^2  \cdot 2^4$?  Is the answer closer to  $2^4$, or $2^6$? 
   
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   (10) What is $10^4 \cdot  10^8$?  Write it in exponent form as $10^n$ for some number $n$, and also write it out  as a number with all the zeroes. 
   
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   (11) What is $10^1 \cdot 10^1$ in exponent form as $10^n$, and written out as a number?  
          \vspace{80pt }
          
 (12) What is $10^0 \cdot 10^1$  in exponent form as $10^n$, and written out as a number?  
        \vspace{80pt }
        
 (13) What is $10^3 \cdot 10^{-1}$   in exponent form as $10^n$, and written out as a number?  
     
\vspace*{1.5in}
 
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  Answers: (1) $2^2 = 4, 2^3 = 8,  2^4 = 16, 2^1 = 2, 2^0=1, 2^{-1} =  \frac{1}{2}, 2^{-2} = \frac{1}{4}.$ \\
  (2) $3^2 = 9, 3^3 = 27,  3^4 = 81, 3^1 = 3, 3^0=1, 3^{-1} =  \frac{1}{3}, 3^{-2} = \frac{1}{9}.$ \\
  (3)  $5^2 = 25, 5^3 = 125,  5^4 =625, 5^1 = 5, 5^0=1, 5^{-1} =  \frac{1}{5}, 5^{-2} = \frac{1}{25}.$\\
  (4) $10^2 = 100, 10^3 = 1,000,  10^4 = 10,000, 10^1 = 10, 10^0=1, 10^{-1} =  \frac{1}{10}, 10^{-2} = \frac{1}{100}.$\\
   (5) The number of zeroes equals the exponent for positive exponents.  \\
    (6) $3^2 + 3^1 = 9 + 3 = 12$\\
      (7)  $3^2 \cdot 3^1 = 9  \cdot  3 = 27 = 3^3$. 
   
 
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