Prime Factorisation

Step 1: Write (3360=32\times105). Step 2: (32=2^5) and (105=3\times5\times7), so (3360=2^5\times3\times5\times7). Step 3: Do not keep 105 in the final form.

Step 1: Write (1260=126\times10). Step 2: (126=2\times3^2\times7) and (10=2\times5), so the total power of 2 is 2. Step 3: Therefore, (a=2).

Step 1: (1350=27\times50). Step 2: (27=3^3) and (50=2\times5^2), so (1350=2\times3^3\times5^2). Step 3: Comparing gives (b=3).

Step 1: Write (1500=15\times100). Step 2: (15=3\times5) and (100=2^2\times5^2), so the power of 2 is 2. Step 3: Comparing gives (p=2).

Step 1: (2100=21\times100). Step 2: (21=3\times7) and (100=2^2\times5^2), so the power of 5 is 2. Step 3: Therefore, (q=2).

Step 1: Calculate (2^3=8) and (3^2=9). Step 2: (8\times9\times11=792). Step 3: Solve prime powers first, then multiply.

Step 1: Calculate (2^4=16). Step 2: (16\times3\times5\times7=1680). Step 3: When there are four factors, multiply smaller products in order.

Step 1: Calculate (3^3=27). Step 2: (2\times27\times5\times7=1890). Step 3: Finding the value of the power first makes calculation simple.

Step 1: Calculate (2^2=4) and (3^2=9). Step 2: (4\times9\times7\times11=2772). Step 3: First multiply 4 and 9, then include the remaining factors.

Step 1: Calculate (2^4=16) and (3^3=27). Step 2: (16\times27\times7=3024). Step 3: Simplify higher powers separately and multiply.

Step 1: (2^2=4) and (5^2=25). Step 2: (4\times3\times25\times7=2100). Step 3: Solving the powers first makes multiplication easier.

Step 1: Calculate (2^3=8) and (3^2=9). Step 2: (8\times9\times5\times7=2520). Step 3: First solve powers, then multiply by the remaining factors.

Step 1: In the final form, bases should be prime only. Step 2: In the first option, bases 2, 3, and 11 are prime. Step 3: 16, 9, 99, and 18 are composite, so they are not final forms.

Step 1: A final prime factorisation should not contain a composite factor like 25. Step 2: Since (25=5^2), (2^2\times25\times7) is not final form. Step 3: Change 25 into (5^2).

Step 1: Divide 4096 repeatedly by 2. Step 2: Twelve factors of 2 give (4096=2^{12}). Step 3: 64 and 16 are composite, so write (2^{12}) as the final prime form.

Step 1: Divide 6561 repeatedly by 3. Step 2: Eight factors of 3 give (6561=3^8). Step 3: 81 and 27 are composite, so write a power of 3 in the final form.

Step 1: Write (2197=13\times169). Step 2: (169=13^2), so (2197=13^3). Step 3: Since 169 is composite, write (13^3) in the final form.

Step 1: Write (6250=625\times10). Step 2: (625=5^4) and (10=2\times5), so (6250=2\times5^5). Step 3: Count the total power of 5 as 5.

Step 1: Write (5103=729\times7). Step 2: (729=3^6), so (5103=3^6\times7). Step 3: Do not leave 729 in the final form; write it as a power of 3.

Step 1: Write (5488=16\times343). Step 2: (16=2^4) and (343=7^3), so (5488=2^4\times7^3). Step 3: Convert 16 and 343 into prime powers.