simplify (x^6y^9)/(x^2y^5)

{ "query": { "display": "simplify $$\\frac{x^{6}y^{9}}{x^{2}y^{5}}$$", "symbolab_question": "SIMPLIFY#simplify \\frac{x^{6}y^{9}}{x^{2}y^{5}}" }, "solution": { "level": "PERFORMED", "subject": "Algebra", "topic": "Algebra", "subTopic": "Simplify", "default": "x^{4}y^{4}", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "Simplify $$\\frac{x^{6}y^{9}}{x^{2}y^{5}}:{\\quad}x^{4}y^{4}$$", "input": "\\frac{x^{6}y^{9}}{x^{2}y^{5}}", "steps": [ { "type": "interim", "title": "Simplify $$\\frac{x^{6}}{x^{2}}:{\\quad}x^{4}$$", "input": "\\frac{x^{6}}{x^{2}}", "steps": [ { "type": "step", "primary": "Apply exponent rule: $$\\frac{x^{a}}{x^{b}}=x^{a-b}$$", "result": "=x^{6-2}", "meta": { "practiceLink": "/practice/exponent-practice", "practiceTopic": "Expand FOIL" } }, { "type": "step", "primary": "Subtract the numbers: $$6-2=4$$", "result": "=x^{4}" } ], "meta": { "solvingClass": "Solver2", "interimType": "Generic Simplify Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7gdZhste3KGS02t5SFPRMydSUzgALSYbl/aGC/IIM1p+rju+5Z51e/ZZSD3gRHwjB2xlVOJxVve7UyZKmYIFNBXql8XXPq6bNQlMm+36iNhljgtURsNZ8mF2q2lQDr86HqV+AMg7bQ9Uc3OOJ+3Ex3b8yD3hLQ33B7/8/LpbPE3o=" } }, { "type": "step", "result": "=\\frac{x^{4}y^{9}}{y^{5}}" }, { "type": "interim", "title": "Simplify $$\\frac{y^{9}}{y^{5}}:{\\quad}y^{4}$$", "input": "\\frac{y^{9}}{y^{5}}", "steps": [ { "type": "step", "primary": "Apply exponent rule: $$\\frac{x^{a}}{x^{b}}=x^{a-b}$$", "result": "=y^{9-5}", "meta": { "practiceLink": "/practice/exponent-practice", "practiceTopic": "Expand FOIL" } }, { "type": "step", "primary": "Subtract the numbers: $$9-5=4$$", "result": "=y^{4}" } ], "meta": { "solvingClass": "Solver2", "interimType": "Generic Simplify Specific 1Eq", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s736qHsa+/ePgJWWI8LbnCpROaXhUnHVSAel3wknhF04Crju+5Z51e/ZZSD3gRHwjBS0jYYQY6KwaFPNR8Ms2QIHql8XXPq6bNQlMm+36iNhljgtURsNZ8mF2q2lQDr86H7d4nIzQAalVIQNKeTrjrOb8yD3hLQ33B7/8/LpbPE3o=" } }, { "type": "step", "result": "=x^{4}y^{4}" } ], "meta": { "solvingClass": "Solver2" } }, "meta": { "showVerify": true } }