shcards","topicId":"48b8b089-f0bb-40c5-aeb7-3c5a11cf2288","topicSlug":"algebra-and-functions-2","cards":[{"id":"1cef84e1-fae7-4b59-8fb5-031a1bc75bb2","cardType":"cloze","front":"For the same base, multiplying powers gives $a^m a^n=$ $\\text{[...]}$.","back":"For the same base, multiplying powers gives $a^m a^n=$ $\\boxed{a^{m+n}}$.","points":null,"mcqOptions":null},{"id":"0134fa81-5371-43cd-875e-b9551ca84cd4","cardType":"cloze","front":"For $a\\neq0$, dividing powers gives $\\frac{a^m}{a^n}=$ $\\text{[...]}$.","back":"For $a\\neq0$, dividing powers gives $\\frac{a^m}{a^n}=$ $\\boxed{a^{m-n}}$.","points":null,"mcqOptions":null},{"id":"c88fdaa2-c2c0-4159-936a-77425e547227","cardType":"cloze","front":"Raising a power to a power gives $(a^m)^n=$ $\\text{[...]}$.","back":"Raising a power to a power gives $(a^m)^n=$ $\\boxed{a^{mn}}$.","points":null,"mcqOptions":null},{"id":"77dc35d4-efb0-42a5-836d-6d2b54922af0","cardType":"basic","front":"Simplify $2^3\\cdot3^3$.","back":"$6^3$, by distributing the common exponent.","points":1,"mcqOptions":null},{"id":"21aafbca-e877-4920-b833-733832e0f67e","cardType":"cloze","front":"For any non-zero base, $a^0=$ $\\text{[...]}$.","back":"For any non-zero base, $a^0=$ $\\boxed{1}$.","points":null,"mcqOptions":null},{"id":"e5520051-e9d2-44f7-83a4-407ff2a318ae","cardType":"basic","front":"What value is assigned to $0^0$ at this level?","back":"It is normally undefined.","points":1,"mcqOptions":null},{"id":"53b0de6b-d459-4bc9-bf07-f4696f2223c8","cardType":"cloze","front":"A negative index represents a reciprocal: $a^{-n}=$ $\\text{[...]}$, where $a\\neq0$.","back":"A negative index represents a reciprocal: $a^{-n}=$ $\\boxed{\\frac{1}{a^n}}$, where $a\\neq0$.","points":null,"mcqOptions":null},{"id":"32228d6a-3b58-4bd4-90e5-1e46f7ec723f","cardType":"basic","front":"Evaluate $2^{-3}$.","back":"$\\frac18$.","points":1,"mcqOptions":null},{"id":"6ac757d2-6ade-4b3e-912c-3b23b1ec08c9","cardType":"cloze","front":"For positive $a$ and positive integer $n$, $a^{1/n}=$ $\\text{[...]}$.","back":"For positive $a$ and positive integer $n$, $a^{1/n}=$ $\\boxed{\\sqrt[n]{a}}$.","points":null,"mcqOptions":null},{"id":"59b8cfc7-2a51-4521-bd9a-89623bff6fa9","cardType":"basic","front":"In $a^{m/n}$, which operation is determined by the denominator $n$?","back":"Take the $n$th root.","points":1,"mcqOptions":null},{"id":"a7695ac0-833b-425b-91a5-b971f27b78c0","cardType":"basic","front":"Evaluate $8^{2/3}$.","back":"$4$.","points":1,"mcqOptions":null},{"id":"56264b15-8d32-46de-95ea-a197b58a0598","cardType":"basic","front":"Evaluate $27^{-2/3}$.","back":"$\\frac19$.","points":1,"mcqOptions":null},{"id":"f8db9257-e796-405c-b17b-f89b559ccd6b","cardType":"basic","front":"Why does $(-4)^{1/2}$ have no real value?","back":"An even root of a negative number is not real.","points":2,"mcqOptions":null},{"id":"3f027634-e0c6-4e55-b6c0-d5e30921bacf","cardType":"basic","front":"Evaluate $(-8)^{1/3}$ over the real numbers.","back":"$-2$.","points":1,"mcqOptions":null},{"id":"0544b6a1-4517-47bb-9fa8-002c53051e7e","cardType":"basic","front":"Simplify $\\frac{x^{5/6}x^{1/2}}{x^{1/3}}$ for $x>0$.","back":"$x$.","points":2,"mcqOptions":null},{"id":"4204d391-6de1-43c0-bb0e-6c39215d8121","cardType":"basic","front":"Write $\\frac{6x^{-3}y^2}{2y^{-1}}$ using positive indices.","back":"$\\frac{3y^3}{x^3}$.","points":2,"mcqOptions":null},{"id":"951a8b74-d785-4507-993b-51f3bdd1bc8f","cardType":"basic","front":"Simplify $\\frac{(x^3)^4x^{-2}}{x^5}$, where $x\\neq0$.","back":"$x^5$.","points":2,"mcqOptions":null},{"id":"f6f8f88a-6ba9-4528-8791-31d14b90d327","cardType":"basic","front":"Simplify $\\frac{x^{3/4}x^{1/2}}{x^{-1/4}}$ as a single positive power.","ba

1.1.1 Algebra and functions Flashcards

1.1.1 Algebra and functions Flashcards