simplify (-125)^{1/3}

{ "query": { "display": "simplify $$\\left(-125\\right)^{\\frac{1}{3}}$$", "symbolab_question": "SIMPLIFY#simplify (-125)^{\\frac{1}{3}}" }, "solution": { "level": "PERFORMED", "subject": "Algebra", "topic": "Algebra", "subTopic": "Simplify", "default": "-5", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\left(-125\\right)^{\\frac{1}{3}}=-5$$", "input": "\\left(-125\\right)^{\\frac{1}{3}}", "steps": [ { "type": "step", "primary": "Apply exponent rule: $$\\left(-a\\right)^{\\frac{1}{n}}=-\\left(a\\right)^{\\frac{1}{n}},\\:\\quad$$if $$n$$ is odd", "secondary": [ "$$\\left(-125\\right)^{\\frac{1}{3}}=-125^{\\frac{1}{3}}$$" ], "result": "=-125^{\\frac{1}{3}}" }, { "type": "step", "primary": "Factor the number: $$125=5^{3}$$", "result": "=-\\left(5^{3}\\right)^{\\frac{1}{3}}" }, { "type": "step", "primary": "Apply exponent rule: $$\\left(a^{b}\\right)^{c}=a^{bc},\\:\\quad\\:a\\ge0$$", "secondary": [ "$$\\left(5^{3}\\right)^{\\frac{1}{3}}=5^{3\\cdot\\:\\frac{1}{3}}$$" ], "result": "=-5^{3\\cdot\\:\\frac{1}{3}}" }, { "type": "interim", "title": "$$3\\cdot\\:\\frac{1}{3}=1$$", "input": "3\\cdot\\:\\frac{1}{3}", "steps": [ { "type": "step", "primary": "Convert element to fraction: $$3=\\frac{3}{1}$$", "result": "=\\frac{3}{1}\\cdot\\:\\frac{1}{3}" }, { "type": "step", "primary": "Cross-cancel: $$3$$", "result": "=1" } ], "meta": { "solvingClass": "Solver", "interimType": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7CzXS+MvaOUdKL6IkXGMFAzFIXl/yolDRhu0cz3GobRqrju+5Z51e/ZZSD3gRHwjBE9/03SOiEv+BIHutWLr6nVjLxBb7GnxOcfSgBEBJAkMamNHtKnaF5YXcjbsOcLVr" } }, { "type": "step", "result": "=-5^{1}" }, { "type": "step", "primary": "Apply exponent rule: $$a^{1}=a$$", "secondary": [ "$$5^{1}=5$$" ], "result": "=-5", "meta": { "practiceLink": "/practice/exponent-practice", "practiceTopic": "Expand FOIL" } } ], "meta": { "solvingClass": "Solver2" } }, "meta": { "showVerify": true } }