simplify 6/(\sqrt[3]{x)}

{ "query": { "display": "simplify $$\\frac{6}{\\sqrt[3]{x}}$$", "symbolab_question": "SIMPLIFY#simplify \\frac{6}{\\sqrt[3]{x}}" }, "solution": { "level": "PERFORMED", "subject": "Algebra", "topic": "Algebra", "subTopic": "Simplify", "default": "\\frac{6x^{\\frac{2}{3}}}{x}", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "$$\\frac{6}{\\sqrt[3]{x}}=\\frac{6x^{\\frac{2}{3}}}{x}$$", "input": "\\frac{6}{\\sqrt[3]{x}}", "steps": [ { "type": "step", "primary": "Multiply by the conjugate $$\\frac{x^{\\frac{2}{3}}}{x^{\\frac{2}{3}}}$$", "result": "=\\frac{6x^{\\frac{2}{3}}}{\\sqrt[3]{x}x^{\\frac{2}{3}}}", "meta": { "title": { "extension": "To rationalize the denominator, multiply numerator and denominator by the conjugate of the radical $$\\sqrt[3]{x}$$" } } }, { "type": "interim", "title": "$$\\sqrt[3]{x}x^{\\frac{2}{3}}=x$$", "input": "\\sqrt[3]{x}x^{\\frac{2}{3}}", "result": "=\\frac{6x^{\\frac{2}{3}}}{x}", "steps": [ { "type": "step", "primary": "Apply exponent rule: $$a^b\\cdot\\:a^c=a^{b+c}$$", "secondary": [ "$$x^{\\frac{2}{3}}\\sqrt[3]{x}=\\:x^{\\frac{2}{3}}x^{\\frac{1}{3}}=\\:x^{\\frac{2}{3}+\\frac{1}{3}}$$" ], "result": "=x^{\\frac{2}{3}+\\frac{1}{3}}", "meta": { "practiceLink": "/practice/exponent-practice", "practiceTopic": "Expand FOIL" } }, { "type": "interim", "title": "Join $$\\frac{2}{3}+\\frac{1}{3}:{\\quad}1$$", "input": "\\frac{2}{3}+\\frac{1}{3}", "result": "=x^{1}", "steps": [ { "type": "step", "primary": "Since the denominators are equal, combine the fractions: $$\\frac{a}{c}\\pm\\frac{b}{c}=\\frac{a\\pm\\:b}{c}$$", "result": "=\\frac{2+1}{3}" }, { "type": "step", "primary": "Refine", "result": "=1" } ], "meta": { "interimType": "Algebraic Manipulation Join Concise Title 1Eq" } }, { "type": "step", "primary": "Apply rule $$a^{1}=a$$", "result": "=x" } ], "meta": { "solvingClass": "Solver", "interimType": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7T1YB7PSs5J1lvzYk1s2yuVQIffbADZ/Onu/+b4hFMwdV00rpv8+ZC6TM10tVCSHsSCaXHChELvqKoz6wVAJrHYY+spUsB4yZJkDyh9+Pu3+GaOXoRpEJwDQak/2ah3M16du+hwf9/B9SUl1JQe3HRw==" } } ], "meta": { "solvingClass": "Solver" } }, "meta": { "showVerify": true } }