Answer :
[tex] B. 16 {a}^{2}c[/tex]
step-by-step explanation :
[tex] 48 {a}^{3}b{c}^{2} \div 3abc[/tex]
This can be rewritten as:
[tex] \frac{ 48 {a}^{3}b {c}^{2} }{3abc} [/tex]
Now,
[tex] \frac{48}{3}=16[/tex]
The law of indices states that:
[tex] \frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n} [/tex]
It implies that, when dividing two expressions with the same bases, repeat one of the bases and subtract the exponents.
Therefore,
[tex] \frac{ {a}^{3} }{a}= {a}^{3 - 1} = {a}^{2}[/tex]
[tex]\frac{b}{b} = {b}^{1 - 1} = {b}^{0} = 1[/tex]
Note: Any non-zero number exponent zero is 1
Also
[tex]\frac{ {c}^{2} }{c} = {c}^{2 - 1} = {c}^{1} = c[/tex]
Hence:
[tex] \frac{ 48 {a}^{3}b {c}^{2} }{3abc} = 16 {a}^{2}c[/tex]
