Question

What is the value of $6{{x}^{2}}yz\div 3xy$?
(a) $2yz$
(b) $2zx$
(c) $2{{x}^{2}}z$
(d) $2{{y}^{2}}z$

Answer 1

Hint: First of all separate the constant terms from the expression and write 6 in the numerator and 3 in the denominator. Cancel the common factors present in them. Now, simplify the terms containing the variables. Use the formula of exponents given as ${{a}^{m}}\div {{a}^{n}}={{a}^{m-n}}$ to simplify the exponent of each variable separately.

Complete step by step answer:
Here we have been provided with the expression $6{{x}^{2}}yz\div 3xy$ and we are asked to find its value. Here, we will use some basic formulas of the exponents. Let us assume the given expression as E, so we have,
$\begin{align}
  & \Rightarrow E=6{{x}^{2}}yz\div 3xy \\
 & \Rightarrow E=\dfrac{6{{x}^{2}}yz}{3xy} \\
\end{align}$
We can separate the constant terms and the similar variables and write the above expression as: -
\[\Rightarrow E=\dfrac{6}{3}\times \dfrac{{{x}^{2}}}{x}\times \dfrac{y}{y}\times z\]
Cancelling the common factors of the constant terms and simplifying we get,
\[\Rightarrow E=2\times \dfrac{{{x}^{2}}}{x}\times \dfrac{y}{y}\times z\]
Now, in the term containing the variable x we have its exponent equal to 2 in the numerator and 1 in the denominator, in the variable y the exponent is 1 in both numerator and the denominator while in the variable z the exponent is 1 in the numerator and 0 in the denominator. Therefore, we can leave the variable z and we need to simplify variable x and y. Using the formula of exponent given as ${{a}^{m}}\div {{a}^{n}}={{a}^{m-n}}$ we get,
\[\begin{align}
  & \Rightarrow E=2\times {{x}^{2-1}}\times {{y}^{1-1}}\times z \\
 & \Rightarrow E=2\times {{x}^{1}}\times {{y}^{0}}\times z \\
\end{align}\]
We know that ${{a}^{0}}=1$, so we get,
\[\begin{align}
  & \Rightarrow E=2\times x\times 1\times z \\
 & \therefore E=2xz \\
\end{align}\]

So, the correct answer is “Option b”.

Note: You must remember all the basic formulas of ‘exponents and powers’ like: - \[{{x}^{m}}\times {{x}^{n}}={{x}^{m+n}}\], \[{{x}^{m}}\div {{x}^{n}}={{x}^{m-n}}\], \[{{\left( {{x}^{m}} \right)}^{n}}={{x}^{m\times n}}\], \[{{x}^{-m}}=\dfrac{1}{{{x}^{m}}}\] etc, as they are used in certain other topics of mathematics. Do not forget to cancel the common factors whenever possible. This will get your answer in the simplest form otherwise sometimes if the common factors are not cancelled the answer may be marked incomplete.