Question

$9^6 \times 12^4 \times 7^7$

എന്ന സംഖ്യയുടെ പ്രൈം ഘടകങ്ങളുടെ ആകെ തുക എത്രയാണ്?

• A. 13
• B. 12
• C. 11
• D. 14

Answer 1

Answer:

B. 12

Express in prime factors

$9=3^2$

$9^6 = (3^2)^6 = 3^{12}$

$12 = 2^2\times3$

$12^4 =(2^2 \times 3)^4 = 2^8 \times 3^4$

$7^7$ is already a prime power

combine all

$9^6 \times 12^4 \times 7^7 = 3^{12}\times(2^8\times3^4)\times7^7$

$= 2^8\times3^{12+4}\times7^7$

$= 2^8\times 3^{16}\times7^7$

The distinct prime factors are 2,3,7

sum of factors = 2 +3 + 7 = 12