Question

Find the quotient.

48a 3 bc 2 ÷ 3abc

A 16a 4b 2c 3
B 16a 2c
C 18a 2c
D 16ac 2

Answer 1

Answer :


`B. 16 {a}^(2)c`

step-by-step explanation :


`48 {a}^(3)b{c}^(2) / 3abc`

This can be rewritten as:


`\frac{ 48 {a}^(3)b {c}^(2) }{3abc}`

Now,


`(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)`


`(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`