MATH SOLVE

5 months ago

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

Accepted Solution

A:

Answer:a = 3, b = 7, c = 2Step-by-step explanation:The Prime Factorization of a Number 49,392[tex]\begin{array}{c|c}49392&2\\24696&2\\12348&2\\6174&2\\3087&3\\1029&3\\343&7\\49&7\\7&7\\1\end{array}[/tex][tex]49,392=2\cdot2\cdot2\cdot2\cdot3\cdot3\cdot7\cdot7\cdot7=2^4\cdot3^2\cdot7^3\\\\49,392=a^2\times b^3\times c^4\to a^2\times b^3\times c^4=3^2\cdot7^3\cdot2^4[/tex]Thereforea = 3, b = 7, c = 2