simplify x^{-1/2}*x

{ "query": { "display": "simplify $$x^{-\\frac{1}{2}}\\cdot\\:x$$", "symbolab_question": "SIMPLIFY#simplify x^{-\\frac{1}{2}}\\cdot x" }, "solution": { "level": "PERFORMED", "subject": "Algebra", "topic": "Algebra", "subTopic": "Simplify", "default": "x^{\\frac{1}{2}}", "meta": { "showVerify": true } }, "steps": { "type": "interim", "title": "Simplify $$x^{-\\frac{1}{2}}\\cdot\\:x:{\\quad}x^{\\frac{1}{2}}$$", "input": "x^{-\\frac{1}{2}}x", "steps": [ { "type": "step", "primary": "Apply exponent rule: $$a^b\\cdot\\:a^c=a^{b+c}$$", "secondary": [ "$$x^{-\\frac{1}{2}}x=x^{-\\frac{1}{2}+1}$$" ], "result": "=x^{-\\frac{1}{2}+1}", "meta": { "practiceLink": "/practice/exponent-practice", "practiceTopic": "Expand FOIL" } }, { "type": "interim", "title": "$$-\\frac{1}{2}+1=\\frac{1}{2}$$", "input": "-\\frac{1}{2}+1", "steps": [ { "type": "step", "primary": "Convert element to fraction: $$1=\\frac{1\\cdot\\:2}{2}$$", "result": "=-\\frac{1}{2}+\\frac{1\\cdot\\:2}{2}" }, { "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{-1+1\\cdot\\:2}{2}" }, { "type": "interim", "title": "$$-1+1\\cdot\\:2=1$$", "input": "-1+1\\cdot\\:2", "steps": [ { "type": "step", "primary": "Multiply the numbers: $$1\\cdot\\:2=2$$", "result": "=-1+2" }, { "type": "step", "primary": "Add/Subtract the numbers: $$-1+2=1$$", "result": "=1" } ], "meta": { "solvingClass": "Solver", "interimType": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7vn6CQNwxYfV8gDG5KuxmLlXTSum/z5kLpMzXS1UJIexiYFOaxxQqg3o8CNKkTm2qk4XEODzDfV3RCKyB8F0QybUZ0qCI2z4+iUq9O5bNiT8=" } }, { "type": "step", "result": "=\\frac{1}{2}" } ], "meta": { "solvingClass": "Solver", "interimType": "Solver", "gptData": "pG0PljGlka7rWtIVHz2xymbOTBTIQkBEGSNjyYYsjjDErT97kX84sZPuiUzCW6s7wUp83naOOyePooOzBcIRVkEgyJ/p2vjjBqmu8hs9cBRCyVMMrE5H/on5k4a9Rxq6ndjfX1glbMVRzeUP1QBSbah0PrGQGSPs3zioY12E5hikQXilCmYoz1KkVtub16lEzUWg4Vd23F433IX/OPT+HA==" } }, { "type": "step", "result": "=x^{\\frac{1}{2}}" } ], "meta": { "solvingClass": "Solver2" } }, "meta": { "showVerify": true } }