{"id":"9f6cae61-fcbc-4b4a-bbc7-52f64fa3a42e","revisionId":"b9b3a2d7-9cdb-4818-b203-ea1b7b2fa444","questionNumber":"14","questionType":"LA","specification":"","difficulty":2,"difficultyBand":"hard","totalMarks":5,"sourceTitle":"Indices","calculatorUse":"non_calc","parts":[{"id":"266dee37-30da-429a-b643-2f9c67950f1c","label":"a","content":"Simplify $p^3 \\times p^5$","markscheme":"- $p^8$ B1","marks":1,"order":0,"markingRubric":{"totalMarks":1,"points":[{"id":"p1","marks":1,"description":"$$p^8$","code":"B"}],"finalAnswers":["p^8"],"generatedAt":"2026-05-06T01:49:23.623Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"add_the_indices","label":"Add the indices","steps":[{"type":"text","order":0,"title":"Spot the same base","content":"Both powers have the same base, $p$. When multiplying powers with the same base, keep the base and add the indices. An **index** is the small raised number showing the power.","highlights":[{"text":"$$p^3 \\times p^5$","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$p^3 \\times p^5 = p^{\\htmlData{anchor=indices}{\\color{@sky}{3+5}}}$"},{"latex":"$$p^{3+5} = \\htmlData{anchor=result}{\\color{@sky}{p^8}}$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"indices"},{"color":"sky","style":"text-color","anchor":"result"}],"connections":[{"to":"result","from":"indices","color":"sky","label":"add"}]},"order":1,"title":"Add the indices","description":"Apply the rule for multiplying powers with the same base. The final result shown below earns the B1 mark."}]}],"generatedAt":"2026-07-20T10:35:10.341Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]},{"id":"e0f98185-aeb2-4a6f-abd2-ea845c082015","label":"b","content":"Simplify $(4ab^2)^3$","markscheme":"- For two of 64, $a^3$, or $b^6$ M1\n- $64a^3b^6$ A1","marks":2,"order":1,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Correctly simplifies at least two components of the expression (e.g., 64, $a^3$, or $b^6$).","code":"M"},{"id":"p2","marks":1,"description":"$$64a^3b^6$","code":"A"}],"finalAnswers":["64a^3b^6"],"generatedAt":"2026-05-06T01:49:23.623Z","modelVersion":"gemini-3-flash-preview"},"explanation":{"methods":[{"id":"power_of_a_product","label":"Power of a product","steps":[{"type":"text","order":0,"title":"Apply the power","content":"The outside power applies to **every factor** inside the brackets:\n\n$$(4ab^2)^3=4^3\\times a^3\\times (b^2)^3$$","highlights":[{"text":"Simplify $(4ab^2)^3$","location":"specification"}]},{"type":"hyper_latex","block":{"nodes":[{"latex":"$$\\htmlData{anchor=coeff_start}{\\color{@sky}{4^3}}$"},{"latex":"$$\\htmlData{anchor=coeff_result}{\\color{@sky}{64}}$"},{"latex":"$$\\htmlData{anchor=b_start}{\\color{@orange}{b^{2\\times 3}}}$"},{"latex":"$$\\htmlData{anchor=b_result}{\\color{@orange}{b^6}}$"},{"latex":"$$64a^3b^6$"}],"highlights":[{"color":"sky","style":"text-color","anchor":"coeff_start"},{"color":"sky","style":"text-color","anchor":"coeff_result"},{"color":"orange","style":"text-color","anchor":"b_start"},{"color":"orange","style":"text-color","anchor":"b_result"}],"connections":[{"to":"coeff_result","from":"coeff_start","color":"sky","style":"solid"},{"to":"b_result","from":"b_start","color":"orange","style":"solid"}]},"order":1,"title":"Evaluate the powers","description":"Calculate the coefficient and the power of b separately. Obtaining any two of 64, a³ and b⁶ earns M1. Combining all three to give 64a³b⁶ earns A1."}]}],"generatedAt":"2026-07-20T10:47:03.848Z","modelVersion":"gpt-5.6-sol","explanationVersion":"v3"},"options":[]},{"id":"d138084b-9e5a-4011-b669-1c72dfc280b6","label":"c","content":"Simplify $\\frac{16m^7n^3}{4m^3n}$","markscheme":"- For two of 4, $m^4$, or $n^2$ M1\n- $4m^4n^2$ A1","marks":2,"order":2,"markingRubric":{"totalMarks":2,"points":[{"id":"p1","marks":1,"description":"Correctly simplifies at least two components of the expression (e.g., 4, $m^4$, or $n^2$).","code":"M"},{"id":"

Indices Questions

Indices Questions

Indices Questions

Indices Questions