Prime Factorisation

Step 1: (2^4=16). Step 2: (16\times3\times5\times11=2640). Step 3: Multiply all factors to get the number from prime form.

Step 1: (3^4=81). Step 2: (81\times5\times7=2835). Step 3: Simplifying the power first keeps the calculation clear.

Step 1: In final prime form, bases should be prime. Step 2: In the first option, 2, 3, and 7 are prime bases. Step 3: 4, 81, 567, 12, and 189 are composite, so they are not final forms.

Step 1: Final prime factorisation must not contain a composite factor. Step 2: 195 is composite and (195=3\times5\times13). Step 3: Therefore, (2^4\times195) is not final form.

Step 1: Write (7776=32\times243). Step 2: (32=2^5) and (243=3^5), so (7776=2^5\times3^5). Step 3: 32 and 243 are composite, so write prime bases in the final form.

Step 1: (10000) can be written as (10^4). Step 2: Since (10=2\times5), (10^4=2^4\times5^4). Step 3: 10 is composite, so write powers of 2 and 5 in the final form.

Step 1: Write (4913=17\times289). Step 2: (289=17^2), so (4913=17^3). Step 3: Since 289 is composite, write (17^3) in the final form.

Step 1: Write (12500=125\times100). Step 2: (125=5^3) and (100=2^2\times5^2), so (12500=2^2\times5^5). Step 3: Count the total power of 5 as 5.

Step 1: Write (10206=2\times5103). Step 2: (5103=3^6\times7), so (10206=2\times3^6\times7). Step 3: Convert 5103 into prime powers.

Step 1: Write (13720=40\times343). Step 2: (40=2^3\times5) and (343=7^3), so (13720=2^3\times5\times7^3). Step 3: Write 40 and 343 in prime form.

Step 1: Calculate (2^5=32) and (3^2=9). Step 2: (32\times9\times7=2016). Step 3: Solving powers first gives the answer quickly.

Step 1: Calculate (3^2=9) and (7^2=49). Step 2: (9\times5\times49=2205). Step 3: Simplify the two powers first and multiply.

Step 1: Calculate (2^2=4) and (3^4=81). Step 2: (4\times81\times7=2268). Step 3: Simplifying the higher power first is the right method.

Step 1: Calculate (2^4=16). Step 2: (16\times3\times5\times11=2640). Step 3: Do multiplication in small steps to avoid mistakes.

Step 1: Write (4752=16\times297). Step 2: (16=2^4) and (297=3^3\times11), so (4752=2^4\times3^3\times11). Step 3: Give 297 its complete prime form.

Step 1: Write (5850=18\times325). Step 2: (18=2\times3^2) and (325=5^2\times13), so (5850=2\times3^2\times5^2\times13). Step 3: Avoid decimal forms and use whole factors.

Step 1: Write (7560=756\times10). Step 2: (756=2^2\times3^3\times7) and (10=2\times5), so (7560=2^3\times3^3\times5\times7). Step 3: Count the total power of 2 as 3.

Step 1: Calculate (3^2=9) and (5^2=25). Step 2: (2\times9\times25\times13=5850). Step 3: First do (9\times25=225), then multiply the rest.

Step 1: Divide 16384 repeatedly by 2. Step 2: Fourteen factors of 2 give (16384=2^{14}). Step 3: 128 and 16 are composite, so write the power of 2 in final prime form.

Step 1: In final prime factorisation, the base must be prime. Step 2: 25 is composite and (25=5^2). Step 3: Therefore, (25^2\times7) must be changed into (5^4\times7).