Question

If a^2 x b^3 x c^4 = 49392, what is the value of a, b, and c?

Answer 1

a = 3, b = 7 and c = .2

Explanation:

Lets find the prime factors of 49392:

2 49392

2 24696

2 12348

2 6174

3 3087

3 1029

7 343

7 49

7 7

1

So 49392 = 2^4 * 3^2 * 7^3

Comparing with a^2 * b^3 * c^4 :-

a = 3, b = 7 and c = 2.

Answer 2

a = 3, b = 7, c = 2

Explanation:

The Prime Factorization of a Number 49,392

`\begin{array}c49392&2\\24696&2\\12348&2\\6174&2\\3087&3\\1029&3\\343&7\\49&7\\7&7\\1\end{array}`

`49,392=2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot7\cdot7\cdot7=2^4\cdot3^2\cdot7^3\\\\49,392=a^2* b^3* c^4\to a^2* b^3* c^4=3^2\cdot7^3\cdot2^4`

Therefore

a = 3, b = 7, c = 2