simplify-2^4*5+(16)/((-2)^3)

{ "query": { "display": "simplify $$-2^{4}\\cdot\\:5+\\frac{16}{\\left(-2\\right)^{3}}$$", "symbolab_question": "SIMPLIFY#simplify -2^{4}\\cdot 5+\\frac{16}{(-2)^{3}}" }, "solution": { "level": "PERFORMED", "subject": "Algebra", "topic": "Algebra", "subTopic": "Simplify", "default": "-82", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$-2^{4}\\cdot\\:5+\\frac{16}{\\left(-2\\right)^{3}}=-82$$", "input": "-2^{4}\\cdot\\:5+\\frac{16}{\\left(-2\\right)^{3}}", "steps": [ { "type": "interim", "title": "$$-2^{4}\\cdot\\:5=-80$$", "input": "-2^{4}\\cdot\\:5", "steps": [ { "type": "step", "primary": "$$2^{4}=16$$", "result": "=-16\\cdot\\:5" }, { "type": "step", "primary": "Multiply the numbers: $$-16\\cdot\\:5=-80$$", "result": "=-80" } ], "meta": { "interimType": "N/A" } }, { "type": "interim", "title": "$$\\frac{16}{\\left(-2\\right)^{3}}=-2$$", "input": "\\frac{16}{\\left(-2\\right)^{3}}", "steps": [ { "type": "step", "primary": "Apply exponent rule: $$\\left(-a\\right)^{n}=-a^{n},\\:\\quad$$if $$n$$ is odd", "secondary": [ "$$\\left(-2\\right)^{3}=-2^{3}$$" ], "result": "=\\frac{16}{-2^{3}}" }, { "type": "step", "primary": "Factor the number: $$16=2^{4}$$", "result": "=\\frac{2^{4}}{-2^{3}}" }, { "type": "interim", "title": "$$\\frac{2^{4}}{2^{3}}=2$$", "input": "\\frac{2^{4}}{2^{3}}", "steps": [ { "type": "step", "primary": "Apply exponent rule: $$\\frac{x^{a}}{x^{b}}=x^{a-b}$$", "result": "=2^{4-3}", "meta": { "practiceLink": "/practice/exponent-practice", "practiceTopic": "Expand FOIL" } }, { "type": "step", "primary": "Subtract the numbers: $$4-3=1$$", "result": "=2^{1}" }, { "type": "step", "primary": "Apply exponent rule: $$a^{1}=a$$", "result": "=2", "meta": { "practiceLink": "/practice/exponent-practice", "practiceTopic": "Expand FOIL" } } ], "meta": { "solvingClass": "Solver2", "interimType": "Solver2", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7BwLWisOT7kJzN9boxzNp64M0mGQJPxKEvWt/PTI0XiKrju+5Z51e/ZZSD3gRHwjBSLdINoPD2MyLmUXT+YnlMi/IpDG09RbcmRlzuOh6GH0MU268i1pU2VWrNWGutuTM" } }, { "type": "step", "result": "=\\frac{2}{-1}" }, { "type": "step", "primary": "Apply the fraction rule: $$\\frac{a}{-1}=-a$$", "result": "=-2" } ], "meta": { "interimType": "N/A" } }, { "type": "step", "result": "=-80-2" }, { "type": "step", "primary": "Subtract the numbers: $$-80-2=-82$$", "result": "=-82" } ], "meta": { "solvingClass": "Solver2" } }, "meta": { "showVerify": true } }