13+2[2^2(3^2-2^3)(2^2+1)-15]

{ "query": { "display": "$$13+2[2^{2}\\left(3^{2}-2^{3}\\right)\\left(2^{2}+1\\right)-15]$$", "symbolab_question": "PEMDAS#13+2[2^{2}(3^{2}-2^{3})(2^{2}+1)-15]" }, "solution": { "level": "PERFORMED", "subject": "Pre Algebra", "topic": "Order of Operations", "subTopic": "Other", "default": "23", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$13+2[2^{2}\\left(3^{2}-2^{3}\\right)\\left(2^{2}+1\\right)-15]=23$$", "input": "13+2[2^{2}\\left(3^{2}-2^{3}\\right)\\left(2^{2}+1\\right)-15]", "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 within parentheses $$[2^{2}\\left(3^{2}-2^{3}\\right)\\left(2^{2}+1\\right)-15]\\::{\\quad}5$$", "input": "2^{2}\\left(3^{2}-2^{3}\\right)\\left(2^{2}+1\\right)-15", "steps": [ { "type": "interim", "title": "Calculate within parentheses $$\\left(3^{2}-2^{3}\\right)\\::{\\quad}1$$", "input": "3^{2}-2^{3}", "steps": [ { "type": "interim", "title": "Calculate exponents $$3^{2}\\::{\\quad}9$$", "input": "3^{2}", "steps": [ { "type": "step", "primary": "$$3^{2}=9$$", "result": "=9" } ], "meta": { "interimType": "Pemdas Exponent Step Title 1Eq" } }, { "type": "step", "result": "=9-2^{3}" }, { "type": "interim", "title": "Calculate exponents $$2^{3}\\::{\\quad}8$$", "input": "2^{3}", "steps": [ { "type": "step", "primary": "$$2^{3}=8$$", "result": "=8" } ], "meta": { "interimType": "Pemdas Exponent Step Title 1Eq" } }, { "type": "step", "result": "=9-8" }, { "type": "interim", "title": "Add and subtract (left to right) $$9-8\\::{\\quad}1$$", "input": "9-8", "steps": [ { "type": "step", "primary": "$$9-8=1$$", "result": "=1" } ], "meta": { "interimType": "Pemdas AddSub Step Title 1Eq" } }, { "type": "step", "result": "=1" } ], "meta": { "interimType": "Pemdas Parentheses Step Title 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7Wu6gPFhOcNBms880nRVsU9iaYQZpOXdPOx87FNfCQzNJDGQzOWQ095ltkyvy6zTB5HME1txg8bVw4+JMqyqqG4iIuF6jHWbVEQd6zS5Jw9d6SKc/lABkC7OwQ2fLczcDhdfR1lAhgecZMNMYu4qvSvRX+wdq41Ay+aiOsJUfL2X7W8VMuCMSE40pLdBhon8FrvW6nFp+gJ0+HoQciMYM1f3KvIFDxXcJ/k2ZYSpjMKQ0wrM8rCbkgoXalZ48CoaH" } }, { "type": "step", "result": "=2^{2}\\cdot\\:1\\cdot\\:\\left(2^{2}+1\\right)-15" }, { "type": "interim", "title": "Calculate within parentheses $$\\left(2^{2}+1\\right)\\::{\\quad}5$$", "input": "2^{2}+1", "steps": [ { "type": "interim", "title": "Calculate exponents $$2^{2}\\::{\\quad}4$$", "input": "2^{2}", "steps": [ { "type": "step", "primary": "$$2^{2}=4$$", "result": "=4" } ], "meta": { "interimType": "Pemdas Exponent Step Title 1Eq" } }, { "type": "step", "result": "=4+1" }, { "type": "interim", "title": "Add and subtract (left to right) $$4+1\\::{\\quad}5$$", "input": "4+1", "steps": [ { "type": "step", "primary": "$$4+1=5$$", "result": "=5" } ], "meta": { "interimType": "Pemdas AddSub Step Title 1Eq" } }, { "type": "step", "result": "=5" } ], "meta": { "interimType": "Pemdas Parentheses Step Title 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7WeCKY5cGCDqgzFRCBCIy+mNtGAQuyRD+wKxdvdqCUU8u3bhSRqOAv7Og4tP2PNEYlpeMl9X+ei3Sv0uNJeMyMR8JRslkmU4o2zIYcqLbUP2z1I4G3oEZOhEgu+0z1s2dRFfJqDMvso54+jKNXLlpMNXJd1bamQeShQgR8jfuZb5lPVoQPSBvX4gA/e9GXfe+HwlGyWSZTijbMhhyottQ/YWWMN6R4lv9Lg6COMGCE772pTlDRHMWYJokPq0FhCQU" } }, { "type": "step", "result": "=2^{2}\\cdot\\:1\\cdot\\:5-15" }, { "type": "interim", "title": "Calculate exponents $$2^{2}\\::{\\quad}4$$", "input": "2^{2}", "steps": [ { "type": "step", "primary": "$$2^{2}=4$$", "result": "=4" } ], "meta": { "interimType": "Pemdas Exponent Step Title 1Eq" } }, { "type": "step", "result": "=4\\cdot\\:1\\cdot\\:5-15" }, { "type": "interim", "title": "Multiply and divide (left to right) $$4\\cdot\\:1\\cdot\\:5\\::{\\quad}20$$", "input": "4\\cdot\\:1\\cdot\\:5", "steps": [ { "type": "step", "primary": "$$4\\cdot\\:1=4$$", "result": "=4\\cdot\\:5" }, { "type": "step", "primary": "$$4\\cdot\\:5=20$$", "result": "=20" } ], "meta": { "interimType": "Pemdas MultDiv Step Title 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s72zeORBWp180mwB2AZkZUY2dALQv+1o0UoxlE4FiKq4w9i9oAvf9GdVXNbR3Y4Fbq1o2SXMcP01J2o+iGOwBer3Do2FgNKLDU3THyobcprxR3pe2iyCXMhybJDvO3By6DOxICZoaLtmN86woMhv/0CqbGL4r8gyrNwtPL4d1PvlXvwG93Es1/4AeK2KexCl3r1o2SXMcP01J2o+iGOwBer3Do2FgNKLDU3THyobcprxRgueuPKqLIQiDHUa1asLtrdvmkV73IMhU9ad8lG1OY9Q==" } }, { "type": "step", "result": "=20-15" }, { "type": "interim", "title": "Add and subtract (left to right) $$20-15\\::{\\quad}5$$", "input": "20-15", "steps": [ { "type": "step", "primary": "$$20-15=5$$", "result": "=5" } ], "meta": { "interimType": "Pemdas AddSub Step Title 1Eq" } }, { "type": "step", "result": "=5" } ], "meta": { "interimType": "Pemdas Parentheses Step Title 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s77ldG0orEiCrC6kW50DC5QlsLKUrOI4Skxe4EVUv+zSlFTtseB73L5Qaq8ezZAAOFcBi7b38Ql3VpY8X+Y0rYCWVZIhzvL4w8nPTfMjKbNG9Y6VtvwO2wYPB5V6+htQ9/dCf++CKA3Tkkd74wCLAvvaDHj/3yZ2be45uIm9Zv4Bh4l3fZD0SDKn0m5K1RzBf0RSpN33oxZMojoqvYhvSJAK9snTer3SwqrqZYihpV5r7BxIIdJvRUoRtjBaMkmJRqNvHOs5MJYNcz+uzyBwt+7HNAW+zrVRvuXbDWeG6yjHirXUoiRh+1eu1VH2rTooyh" } }, { "type": "step", "result": "=13+2\\cdot\\:5" }, { "type": "interim", "title": "Multiply and divide (left to right) $$2\\cdot\\:5\\::{\\quad}10$$", "input": "2\\cdot\\:5", "steps": [ { "type": "step", "primary": "$$2\\cdot\\:5=10$$", "result": "=10" } ], "meta": { "interimType": "Pemdas MultDiv Step Title 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7yWOlD0Num6Fwr0zFbgT3OGdrAypr34gkzi59sEv8D9vBdCRZbfcAskaMoDovZtxNsym5GQXPkoys+F5plIbRZ6BAIcILTmvhqghEmqs1XeQ7EgJmhou2Y3zrCgyG//QKEwgRl/3gu0KgiFhteFP0d+/Ab3cSzX/gB4rYp7EKXevWjZJcxw/TUnaj6IY7AF6vcOjYWA0osNTdMfKhtymvFGICP84z2vGZshMpX4zqEXgkt3WiGR7ZaCaXvz77bMjS" } }, { "type": "step", "result": "=13+10" }, { "type": "interim", "title": "Add and subtract (left to right) $$13+10\\::{\\quad}23$$", "input": "13+10", "steps": [ { "type": "step", "primary": "$$13+10=23$$", "result": "=23" } ], "meta": { "interimType": "Pemdas AddSub Step Title 1Eq" } }, { "type": "step", "result": "=23" } ], "meta": { "solvingClass": "Pemdas", "practiceLink": "/practice/order-of-operations-whole-practice", "practiceTopic": "Order of Operations" } }, "meta": { "showVerify": true } }