simplify (5!)/(0!(5-0)!)

{ "query": { "display": "simplify $$\\frac{5!}{0!\\left(5-0\\right)!}$$", "symbolab_question": "SIMPLIFY#simplify \\frac{5!}{0!(5-0)!}" }, "solution": { "level": "PERFORMED", "subject": "Algebra", "topic": "Algebra", "subTopic": "Simplify", "default": "1", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\frac{5!}{0!\\left(5-0\\right)!}=1$$", "input": "\\frac{5!}{0!\\left(5-0\\right)!}", "steps": [ { "type": "step", "primary": "Subtract the numbers: $$5-0=5$$", "result": "=\\frac{5!}{0!\\cdot\\:5!}" }, { "type": "step", "primary": "Cancel the common factor: $$5!$$", "result": "=\\frac{1}{0!}" }, { "type": "interim", "title": "$$\\frac{1}{0!}=1$$", "input": "\\frac{1}{0!}", "steps": [ { "type": "step", "primary": "Apply factorial rule: $$0!=1$$", "result": "=\\frac{1}{1}" }, { "type": "step", "primary": "Apply the fraction rule: $$\\frac{a}{a}=1$$", "result": "=1" } ], "meta": { "solvingClass": "Solver2", "interimType": "Solver2", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7DckMvXlEyJ7JJiosAOzckS061ljBSPJeENOw2efoSWs8auWUd4WNoosLPjGkhvjRR4IEq5gqBo0nbneAsjr1TiKZTUKCA6rVAykCw/wtOUI=" } }, { "type": "step", "result": "=1" } ], "meta": { "solvingClass": "Solver2" } }, "meta": { "showVerify": true } }