-2(-2)^2+(-2)^6-4(-2)+1

{ "query": { "display": "$$-2\\left(-2\\right)^{2}+\\left(-2\\right)^{6}-4\\left(-2\\right)+1$$", "symbolab_question": "PEMDAS#-2(-2)^{2}+(-2)^{6}-4(-2)+1" }, "solution": { "level": "PERFORMED", "subject": "Pre Algebra", "topic": "Order of Operations", "subTopic": "Other", "default": "65", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$-2\\left(-2\\right)^{2}+\\left(-2\\right)^{6}-4\\left(-2\\right)+1=65$$", "input": "-2\\left(-2\\right)^{2}+\\left(-2\\right)^{6}-4\\left(-2\\right)+1", "steps": [ { "type": "step", "primary": "Follow the PEMDAS order of operations", "meta": { "title": { "extension": "P-Parentheses<br/>E-Exponents<br/>M-Multiply<br/>D-Divide<br/>A-Add<br/>S-Subtract" } } }, { "type": "interim", "title": "Calculate exponents $$\\left(-2\\right)^{2}\\::{\\quad}4$$", "input": "\\left(-2\\right)^{2}", "steps": [ { "type": "step", "primary": "Apply exponent rule: $$\\left(-a\\right)^{n}=a^{n},\\:$$if $$n$$ is even", "secondary": [ "$$\\left(-2\\right)^{2}=2^{2}=4$$" ], "result": "=4" } ], "meta": { "interimType": "Pemdas Exponent Step Title 1Eq" } }, { "type": "step", "result": "=-2\\cdot\\:4+\\left(-2\\right)^{6}-4\\left(-2\\right)+1" }, { "type": "interim", "title": "Calculate exponents $$\\left(-2\\right)^{6}\\::{\\quad}64$$", "input": "\\left(-2\\right)^{6}", "steps": [ { "type": "step", "primary": "Apply exponent rule: $$\\left(-a\\right)^{n}=a^{n},\\:$$if $$n$$ is even", "secondary": [ "$$\\left(-2\\right)^{6}=2^{6}=64$$" ], "result": "=64" } ], "meta": { "interimType": "Pemdas Exponent Step Title 1Eq" } }, { "type": "step", "result": "=-2\\cdot\\:4+64-4\\left(-2\\right)+1" }, { "type": "interim", "title": "Multiply and divide (left to right) $$-2\\cdot\\:4\\::{\\quad}-8$$", "input": "-2\\cdot\\:4", "steps": [ { "type": "step", "primary": "$$-2\\cdot\\:4=-8$$", "result": "=-8" } ], "meta": { "interimType": "Pemdas MultDiv Step Title 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7B1X4vX8dvHiwALqm4A+8GHM/cQB6fwoueuwqqVsLk2OTdaV09PMxEKZ9FieghTFwsTcXQs+nSTj8Kwuqla5yl+fzPVdOmLogHrDWS+tcDJtdEJpGwZiV/epxzlHJwcC/EUBMMnXSykItgHavlxy8F/bgWVy8NE8akUdU8HqWqnAdaAKcvHJaNe7Tjfb+jLNhSj14oWPVE3qRHsE0xYXurvZ/VQZLG8iqVw14ODUNmDWrHrUIwJb6vXsHm3DOpHek" } }, { "type": "step", "result": "=-8+64-4\\left(-2\\right)+1" }, { "type": "interim", "title": "Multiply and divide (left to right) $$4\\left(-2\\right)\\::{\\quad}-8$$", "input": "4\\left(-2\\right)", "steps": [ { "type": "step", "primary": "Apply rule $$a\\cdot\\:\\left(-b\\right)\\:=\\:-a\\cdot\\:b$$", "secondary": [ "$$4\\left(-2\\right)=-4\\cdot\\:2=-8$$" ], "result": "=-8" } ], "meta": { "interimType": "Pemdas MultDiv Step Title 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7LqNEVV4mTCz2Hd/kkGvPD1/QGtFfLxhvgBU4nhkCZ4wtVzNo+vQLLsmFiyuFCx3xk+sYPV843HYAsibsYKUbab7ug0fyiU4vAfaFA8vmGUhEV8moMy+yjnj6Mo1cuWkwP4pCPLvxbx6PkHkrMEi12DjEl4NEx65NLV53c66fQa92lBIQE6rBE2IBzNz6FnjLZyMiI6pb0S35f1I8IY0ECGgICpty8ZZwGZ1y3DB4Ctg=" } }, { "type": "step", "result": "=-8+64-\\left(-8\\right)+1" }, { "type": "interim", "title": "Add and subtract (left to right) $$-8+64-\\left(-8\\right)+1\\::{\\quad}65$$", "input": "-8+64-\\left(-8\\right)+1", "steps": [ { "type": "step", "primary": "$$-8+64=56$$", "result": "=56-\\left(-8\\right)+1" }, { "type": "step", "primary": "Apply rule $$-\\left(-a\\right)\\:=\\:+a$$", "secondary": [ "$$-\\left(-8\\right)=+8$$" ], "result": "=56+8+1" }, { "type": "step", "primary": "$$56+8=64$$", "result": "=64+1" }, { "type": "step", "primary": "$$64+1=65$$", "result": "=65" } ], "meta": { "interimType": "Pemdas AddSub Step Title 1Eq" } }, { "type": "step", "result": "=65" } ], "meta": { "solvingClass": "Pemdas", "practiceLink": "/practice/order-of-operations-whole-practice", "practiceTopic": "Order of Operations" } }, "meta": { "showVerify": true } }