Question

Find the quotient.

Answer 1

Answer :

$B. 16 {a}^{2}c$

step-by-step explanation :

$48 {a}^{3}b{c}^{2} \div 3abc$

This can be rewritten as:

$\frac{ 48 {a}^{3}b {c}^{2} }{3abc}$

Now,

$\frac{48}{3}=16$

The law of indices states that:

$\frac{ {a}^{m} }{ {a}^{n} } = {a}^{m - n}$

It implies that, when dividing two expressions with the same bases, repeat one of the bases and subtract the exponents.

Therefore,

$\frac{ {a}^{3} }{a}= {a}^{3 - 1} = {a}^{2}$

$\frac{b}{b} = {b}^{1 - 1} = {b}^{0} = 1$

Note: Any non-zero number exponent zero is 1

Also

$\frac{ {c}^{2} }{c} = {c}^{2 - 1} = {c}^{1} = c$

Hence:

$\frac{ 48 {a}^{3}b {c}^{2} }{3abc} = 16 {a}^{2}c$