a6605d-2a51-4d7b-a5cc-a687a1a05264","topicSlug":"laws-of-indices","cards":[{"id":"8fdcf010-1be6-4128-884f-9355da51b1e4","cardType":"basic","front":"Write $x^4$ as repeated multiplication.","back":"$$\\boldsymbol{x\\cdot x\\cdot x\\cdot x}$","points":1,"mcqOptions":null},{"id":"5c67b4a2-01cf-470c-a6a3-6f6bae77e68d","cardType":"cloze","front":"For the same base, the product law is $a^m\\cdot a^n=$ $\\text{[...]}$.","back":"For the same base, the product law is $a^m\\cdot a^n=$ $\\boxed{a^{m+n}}$.","points":null,"mcqOptions":null},{"id":"e71e0f1a-20f9-46a0-b540-b748fae9925a","cardType":"cloze","front":"For $a\\neq 0$, the quotient law is $\\frac{a^m}{a^n}=$ $\\text{[...]}$.","back":"For $a\\neq 0$, the quotient law is $\\frac{a^m}{a^n}=$ $\\boxed{a^{m-n}}$.","points":null,"mcqOptions":null},{"id":"54da3776-1e1f-4615-96b1-7b7bef735347","cardType":"cloze","front":"The power-of-a-power law is $(a^m)^n=$ $\\text{[...]}$.","back":"The power-of-a-power law is $(a^m)^n=$ $\\boxed{a^{mn}}$.","points":null,"mcqOptions":null},{"id":"97bcc8da-aac7-4095-aec7-185d7d49d0af","cardType":"basic","front":"Simplify $x^{5/3}\\cdot x^{-1/2}$.","back":"$$\\boldsymbol{x^{7/6}}$","points":1,"mcqOptions":null},{"id":"1b4dca10-f35f-4bcf-9767-9e60d2a59aaa","cardType":"basic","front":"Simplify $3x^{5/2}\\cdot 4x^{7/3}$.","back":"$$\\boldsymbol{12x^{29/6}}$","points":1,"mcqOptions":null},{"id":"86afa2a9-b524-4506-a2ac-b41a4b51de51","cardType":"basic","front":"Simplify $\\frac{18p^{7/4}q^5}{6p^{1/2}q^8}$ using positive indices.","back":"$$\\boldsymbol{\\frac{3p^{5/4}}{q^3}}$","points":2,"mcqOptions":null},{"id":"22491259-6125-4b01-bf17-94c795eb5d0f","cardType":"basic","front":"Simplify $(8x^6)^{2/3}$ for $x\\geq 0$.","back":"$$\\boldsymbol{4x^4}$","points":2,"mcqOptions":null},{"id":"80caf505-5596-49ec-a110-c289240703a4","cardType":"basic","front":"Apply the index $n$ to the product $(ab)^n$.","back":"$$\\boldsymbol{a^nb^n}$","points":1,"mcqOptions":null},{"id":"9cbb696c-9927-4ab9-86bd-a0010c3e3fa8","cardType":"basic","front":"Apply the index $n$ to $\\left(\\frac{a}{b}\\right)^n$, where $b\\neq 0$.","back":"$$\\boldsymbol{\\frac{a^n}{b^n}}$","points":1,"mcqOptions":null},{"id":"555cefb1-2be6-40b8-86c4-eb18d54986f8","cardType":"basic","front":"Does an index generally distribute over addition: $(a+b)^n=a^n+b^n$?","back":"No - index distribution applies to products and quotients.","points":1,"mcqOptions":null},{"id":"34d77807-a881-4812-9485-969add518601","cardType":"basic","front":"Evaluate $a^0$ when $a\\neq 0$.","back":"$$\\boldsymbol{1}$","points":1,"mcqOptions":null},{"id":"9541d6f7-aba3-42a0-8008-7282cefcfc01","cardType":"basic","front":"Why must $a\\neq 0$ in the zero-index law?","back":"Its derivation uses division by $a^m$, which is undefined for $a=0$.","points":2,"mcqOptions":null},{"id":"dfa6ec0f-56f7-4363-9140-765cb223b08d","cardType":"basic","front":"Rewrite $\\frac{6x^{-2}}{y^{-3}}$ using positive indices.","back":"$$\\boldsymbol{\\frac{6y^3}{x^2}}$","points":1,"mcqOptions":null},{"id":"879df514-0288-410b-937e-7ea73063cac9","cardType":"cloze","front":"A negative index gives a reciprocal: $a^{-n}=$ $\\text{[...]}$, for $a\\neq 0$.","back":"A negative index gives a reciprocal: $a^{-n}=$ $\\boxed{\\frac{1}{a^n}}$, for $a\\neq 0$.","points":null,"mcqOptions":null},{"id":"16a2f598-1ad3-4274-a663-1cf910968087","cardType":"cloze","front":"In $a^{m/n}$, the denominator $n$ gives the [ ] and the numerator $m$ gives the power.","back":"In $a^{m/n}$, the denominator $n$ gives the root and the numerator $m$ gives the power.","points":null,"mcqOptions":null},{"id":"03ea6d24-b579-4911-b9f0-1d405f6dd246","cardType":"basic","front":"Evaluate $81^{3/4}$.","back":"$$\\boldsymbol{27}$","points":1,"mcqOptions":null},{"id":"ad21d4b8-40a8-4b2f-be18-e3b99df4bb46","cardType":"basic","front":"Evaluate $32^{-2/5}$.","back":"$$\\boldsymbol{\\frac{1}{4}}$","points":2,"mcqOptions":null},{"id":"b0c210df-3ebf-4a4d-89a9-3f91d4b9f23

1.5.1 Laws of indices Flashcards

1.5.1 Laws of indices Flashcards