#set document(title: "11.2 Entering Expressions", author: "OpenStax / XYZ Homework")
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== 11.2#h(0.6em)Entering Expressions


    
      
=== Parentheses


      #strong[Order of Operations]: The calculator follows the standard order of operations.


      #examplebox("Example 1")[][
Compute #math.equation(block: false, alt: "2 plus 3 times 4")[$2 + 3 ⋅ 4$]. Press


        #math.equation(block: false, alt: "2")[$2$] +  #math.equation(block: false, alt: "3")[$3$]  #math.equation(block: false, alt: "4")[$4$] ENTER


        Ans. #math.equation(block: false, alt: "14")[$14$]
]


      #examplebox("Example 2")[][
Compute #math.equation(block: false, alt: "open parenthesis 2 plus 3 close parenthesis times 4")[$( 2 + 3 ) ⋅ 4$]. Press


        (  #math.equation(block: false, alt: "2")[$2$]  +  #math.equation(block: false, alt: "3")[$3$]  )    #math.equation(block: false, alt: "4")[$4$] ENTER


        Ans. #math.equation(block: false, alt: "20")[$20$]
]


      #examplebox("Example 3")[][
Compute #math.equation(block: false, alt: "the fraction 1 over 2 times 3")[$display(frac(1, 2 ⋅ 3))$]. Press


        #math.equation(block: false, alt: "1")[$1$]   (  #math.equation(block: false, alt: "2")[$2$]  #math.equation(block: false, alt: "3")[$3$]  )  ENTER


        Ans. #math.equation(block: false, alt: "0.1666666667")[$0.1666666667$]
]


      #examplebox("Example 4")[][
Compute #math.equation(block: false, alt: "the fraction 1 plus 3 over 2")[$display(frac(1 + 3, 2))$]. Press


        (  #math.equation(block: false, alt: "1")[$1$]  +  #math.equation(block: false, alt: "3")[$3$]  )    #math.equation(block: false, alt: "2")[$2$] ENTER


        Ans. #math.equation(block: false, alt: "2")[$2$]
]


    
    
      
=== Exponents and Powers


      #strong[Exponents]:  We use the caret key,  , to enter exponents or powers.


      #examplebox("Example 5")[][
Evaluate #math.equation(block: false, alt: "2 to the power 10")[$2^(10)$].


        #math.equation(block: false, alt: "2")[$2$]  ^  #math.equation(block: false, alt: "10")[$10$] ENTER


        Ans. #math.equation(block: false, alt: "1024")[$1024$]
]


      #strong[Squaring]: There is a short-cut key for squaring,  .


      #examplebox("Example 6")[][
Evaluate #math.equation(block: false, alt: "57 squared")[$57^(2)$].


        #math.equation(block: false, alt: "57")[$57$]  ENTER


        Ans. #math.equation(block: false, alt: "3249")[$3249$]
]


      #strong[Fractional Exponents]: Fractional exponents must be enclosed in parentheses!


      #examplebox("Example 7")[][
Evaluate #math.equation(block: false, alt: "8 to the power 2 / 3")[$8^(2 / 3)$].


        #math.equation(block: false, alt: "8")[$8$]   (  #math.equation(block: false, alt: "2")[$2$]  #math.equation(block: false, alt: "3")[$3$]  )  ENTER


        Ans. #math.equation(block: false, alt: "4")[$4$]
]


    
    
      
=== Roots


      #strong[Square Roots]: We access the square root by pressing 2nd  , and the display shows #math.equation(block: false, alt: "the square root of open parenthesis")[$sqrt(zws) \($]. The calculator automatically gives an open parenthesis for the square root, but not a close parenthesis.


      #examplebox("Example 8")[][
Evaluate #math.equation(block: false, alt: "the square root of 2")[$sqrt(2)$].


        2nd   #math.equation(block: false, alt: "2")[$2$]  )  ENTER


        Ans. #math.equation(block: false, alt: "1.414213562")[$1.414213562$]
]


      #examplebox("Example 9")[][
Evaluate #math.equation(block: false, alt: "the square root of 9 plus 16")[$sqrt(9 + 16)$].


        2nd   #math.equation(block: false, alt: "9")[$9$]  #math.equation(block: false, alt: "16")[$16$]  )  ENTER


        Ans. #math.equation(block: false, alt: "5")[$5$]
]


      In the next example, note that we must enter ) at the end of the radicand to tell the calculator where the radical ends.


      #examplebox("Example 10")[][
Evaluate #math.equation(block: false, alt: "the square root of 9 plus 16")[$sqrt(9) + 16$].


        2nd   #math.equation(block: false, alt: "9")[$9$]  )    #math.equation(block: false, alt: "16")[$16$] ENTER


        Ans. #math.equation(block: false, alt: "19")[$19$]
]


      #strong[Cube Roots]: For cube roots, we press MATH to open the Math menu and press #math.equation(block: false, alt: "4")[$4$] (see Figure).


      #figure(figph[two GC settings], alt: "two GC settings", caption: none)


      #examplebox("Example 11")[][
Compute #math.equation(block: false, alt: "the cube root of 1728")[$root(3, 1728)$].


        MATH #math.equation(block: false, alt: "4")[$" " 4 " "$] #math.equation(block: false, alt: "1728")[$#h(0.167em) 1728 #h(0.167em)$] ) ENTER


        Ans. #math.equation(block: false, alt: "12")[$12$]
]


      For evaluating cube roots and square roots, ) can be omitted if there are no operations following the radical.


      #strong[Other Roots]: For #math.equation(block: false, alt: "n")[$n$]th roots, we press MATH to open the Math menu and press #math.equation(block: false, alt: "5")[$5$] (see Figurea). The calculator symbol for #math.equation(block: false, alt: "n")[$n$]th roots, #math.equation(block: false, alt: "the xth root of")[$root(x, " ")$], does not include an open parenthesis,(. If the radicand includes an operation, we must enclose it in parentheses.


      #examplebox("Example 12")[][
Compute #math.equation(block: false, alt: "the 10th root of 2 times 512")[$root(10, 2 ⋅ 512)$].


        #math.equation(block: false, alt: "10")[$10 #h(0.167em)$]MATH #math.equation(block: false, alt: "5")[$" " 5 " "$] ( #math.equation(block: false, alt: "2")[$2$]  #math.equation(block: false, alt: "512")[$512$] ) ENTER


        Ans. #math.equation(block: false, alt: "2")[$2$]
]


      Notice that we enter the index 10 #emph[before] the radical symbol.


    
    
      
=== Absolute Value


      TI calculators use #math.equation(block: false, alt: "a b s open parenthesis x close parenthesis")[$a b s ( x )$] instead of #math.equation(block: false, alt: "vertical bar x vertical bar")[$| x |$] to denote the absolute value of #math.equation(block: false, alt: "x")[$x$]. The absolute value function is the first entry in the MATH NUM menu (see Figure). The calculator gives ( for the absolute value function, but not ).


      #figure(figph[GC Math NUM menu], alt: "GC Math NUM menu", caption: none)


      #examplebox("Example 13")[][
Evaluate #math.equation(block: false, alt: "the fraction vertical bar 21 times 54 minus 81 vertical bar over minus 9")[$display(frac(| 21 ⋅ 54 − 81 |, − 9))$].


        MATH   ENTER #math.equation(block: false, alt: "21")[$21$]  #math.equation(block: false, alt: "54")[$54$]  #math.equation(block: false, alt: "81")[$81$]  )   (-) #math.equation(block: false, alt: "9")[$9$] ENTER


        Ans. #math.equation(block: false, alt: "minus 117")[$− 117$]
]


    
    
      
=== Scientific Notation


      The TI calculators display numbers in scientific notation when the numbers use too many digits to display.


      #examplebox("Example 14")[][
Compute #math.equation(block: false, alt: "123 , 456 , 789 squared")[$123 , 456 , 789^(2)$]. Enter


        #math.equation(block: false, alt: "123456789")[$123456789$]  ENTER


        Ans. #math.equation(block: false, alt: "1.524157875 E 16")[$1.524157875 " E " 16$]
]


      This is how the calculator displays the number #math.equation(block: false, alt: "1.524157875 times 10 to the power 16")[$1.524157875 × 10^(16)$]. Notice that the power #math.equation(block: false, alt: "10 to the power 16")[$10^(16)$] is displayed as #math.equation(block: false, alt: "E 16")[$" E " 16$].


      To enter a number in scientific form, we use the key labeled #strong[EE], or 2nd  ,.


      #examplebox("Example 15")[][
To enter #math.equation(block: false, alt: "3.26 times 10 to the power 18")[$3.26 × 10^(18)$], use the keying sequence


        #math.equation(block: false, alt: "3.26")[$3.26$] 2nd  , (-) #math.equation(block: false, alt: "18")[$18$] ENTER


        Ans. #math.equation(block: false, alt: "3.26 E")[$3.26 " E"$] #math.equation(block: false, alt: "minus 18")[$− 18$]
]


      
        
==== Troubleshooting


        #figure(figph[GC syntax error screen], alt: "GC syntax error screen", caption: none)


        If your calculator gives you an error message like this, you may have made one of the following common mistakes:


        + Using the negative key, (-), when you wanted the subtraction key,  -, or vice versa.
+ Omitting a ( or ). Each ( should have a matching ).


        Press #math.equation(block: false, alt: "2")[$2$] to #strong[Go to] the error, and see Editing Expressions below.