Find the quotient.48a 3 bc 2 ÷ 3abcA 16a 4b 2c 3B 16a 2cC 18a 2cD 16ac 2

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]