Complete the following without the use of a calculator:
", "advice": "", "rulesets": {}, "extensions": [], "builtin_constants": {"e": true, "pi,\u03c0": true, "i": true, "j": false}, "constants": [], "variables": {"ans1": {"name": "ans1", "group": "Ungrouped variables", "definition": "n[0]-n[1]+n[2]*n[3]+n[4]+mult1*(-1)^power+mult2*(-1)^(power+1)", "description": "", "templateType": "anything", "can_override": false}, "mult1": {"name": "mult1", "group": "Ungrouped variables", "definition": "random(4..12)", "description": "", "templateType": "anything", "can_override": false}, "n": {"name": "n", "group": "Ungrouped variables", "definition": "shuffle(-12..-2)[0..5]", "description": "", "templateType": "anything", "can_override": false}, "power": {"name": "power", "group": "Ungrouped variables", "definition": "random(2..12)", "description": "", "templateType": "anything", "can_override": false}, "mult2": {"name": "mult2", "group": "Ungrouped variables", "definition": "random(4..12)", "description": "", "templateType": "anything", "can_override": false}}, "variablesTest": {"condition": "", "maxRuns": 100}, "ungrouped_variables": ["n", "power", "mult1", "mult2", "ans1"], "variable_groups": [], "functions": {}, "preamble": {"js": "", "css": ""}, "parts": [{"type": "gapfill", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "$\\displaystyle\\var{n[0]}-(\\var{n[1]})--\\var{n[2]}\\times(\\var{n[3]})+\\left(\\frac{\\var{n[4]*n[4]}}{\\var{n[4]}}\\right)+\\var{mult1}(-1)^\\var{power}+\\var{mult2}(-1)^\\var{power+1}$ = [[0]]
", "stepsPenalty": "1", "steps": [{"type": "information", "useCustomName": false, "customName": "", "marks": 0, "scripts": {}, "customMarkingAlgorithm": "", "extendBaseMarkingAlgorithm": true, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "nextParts": [], "suggestGoingBack": false, "adaptiveMarkingPenalty": 0, "exploreObjective": null, "prompt": "There are several ways to approach this. However, I will start working left to right, changing things slowly for the sake of clarity. There is no need to do so many lines when you are attempting this:
\nFirst I will determine the signs:
\n\\begin{align}&\\var{n[0]}-(\\var{n[1]})--\\var{n[2]}\\times(\\var{n[3]})+\\left(\\frac{\\var{n[4]*n[4]}}{\\var{n[4]}}\\right)+\\var{mult1}(-1)^\\var{power}+\\var{mult2}(-1)^\\var{power+1}\\\\
&=\\var{n[0]}\\color{red}{+\\var{abs(n[1])}}--\\var{n[2]}\\times(\\var{n[3]})+\\left(\\frac{\\var{n[4]*n[4]}}{\\var{n[4]}}\\right)+\\var{mult1}(-1)^\\var{power}+\\var{mult2}(-1)^\\var{power+1}\\\\
&=\\var{n[0]}+\\var{abs(n[1])}\\color{red}{-\\var{abs(n[2])}}\\times(\\var{n[3]})+\\left(\\frac{\\var{n[4]*n[4]}}{\\var{n[4]}}\\right)+\\var{mult1}(-1)^\\var{power}+\\var{mult2}(-1)^\\var{power+1}\\\\
&=\\var{n[0]}+\\var{abs(n[1])}\\color{red}{+\\var{abs(n[2]*n[3])}}+\\left(\\frac{\\var{n[4]*n[4]}}{\\var{n[4]}}\\right)+\\var{mult1}(-1)^\\var{power}+\\var{mult2}(-1)^\\var{power+1}\\\\
&=\\var{n[0]}+\\var{abs(n[1])}+\\var{abs(n[2]*n[3])}\\color{red}{-\\var{abs(n[4])}}+\\var{mult1}(-1)^\\var{power}+\\var{mult2}(-1)^\\var{power+1}\\\\
&=\\var{n[0]}+\\var{abs(n[1])}+\\var{abs(n[2]*n[3])}-\\var{abs(n[4])}+\\var{mult1}(\\color{red}{\\var{(-1)^power}})+\\var{mult2}(-1)^\\var{power+1}\\\\
&=\\var{n[0]}+\\var{abs(n[1])}+\\var{abs(n[2]*n[3])}-\\var{abs(n[4])}\\color{red}{\\var{if(2|power,latex('+'),latex('-'))}\\var{abs(mult1)}}+\\var{mult2}(-1)^\\var{power+1}\\\\
&=\\var{n[0]}+\\var{abs(n[1])}+\\var{abs(n[2]*n[3])}-\\var{abs(n[4])}\\var{if(2|power,latex('+'),latex('-'))}\\var{abs(mult1)}+\\var{mult2}(\\color{red}{\\var{(-1)^(power+1)}})\\\\
&=\\var{n[0]}+\\var{abs(n[1])}+\\var{abs(n[2]*n[3])}-\\var{abs(n[4])}\\var{if(2|power,latex('+'),latex('-'))}\\var{abs(mult1)}\\color{red}{\\var{if(2|power,latex('-'),latex('+'))}\\var{abs(mult2)}}\\end{align}
Now I will add/subtract from left to right as required:
\\begin{align}
&\\var{n[0]}+\\var{abs(n[1])}+\\var{abs(n[2]*n[3])}-\\var{abs(n[4])}\\var{if(2|power,latex('+'),latex('-'))}\\var{abs(mult1)}\\var{if(2|power,latex('-'),latex('+'))}\\var{abs(mult2)}\\\\
&=\\color{red}{\\var{n[0]+abs(n[1])}}+\\var{abs(n[2]*n[3])}-\\var{abs(n[4])}\\var{if(2|power,latex('+'),latex('-'))}\\var{abs(mult1)}\\var{if(2|power,latex('-'),latex('+'))}\\var{abs(mult2)}\\\\
&=\\color{red}{\\var{n[0]+abs(n[1])+abs(n[2]*n[3])}}-\\var{abs(n[4])}\\var{if(2|power,latex('+'),latex('-'))}\\var{abs(mult1)}\\var{if(2|power,latex('-'),latex('+'))}\\var{abs(mult2)}\\\\
&=\\color{red}{\\var{n[0]+abs(n[1])+n[2]*n[3]+n[4]}}\\var{if(2|power,latex('+'),latex('-'))}\\var{abs(mult1)}\\var{if(2|power,latex('-'),latex('+'))}\\var{abs(mult2)}\\\\
&=\\color{red}{\\var{n[0]+abs(n[1])+n[2]*n[3]+n[4]+mult1*(-1)^power}}\\var{if(2|power,latex('-'),latex('+'))}\\var{abs(mult2)}\\\\
&=\\color{red}{\\var{ans1}}
\\end{align}