Question

How do you simplify ${\left( {xy{z^2}} \right)^4}$ ?

Answer 1

Solving these types of questions are easy, as all you have to do is separate the variables and then multiply the powers outside the bracket and the individual power. Doing this you will do something like this ${x^4} \times {y^4} \times {z^8}$ which will be the most simplified version of the given question.

Complete step by step answer:
Here, to solve this type of problem the first thing we need to do is separate variables
Now, we know that whenever a number is raised to a power outside the bracket, we can simply write it without brackets if it itself doesn’t have any power. Mathematically we can write it as:-
${\left( a \right)^x} = {a^x}$
Now, whenever there is a power of its own, we will multiply both the powers. Mathematically we will write it as:-
${\left( {{a^y}} \right)^x} = {a^{y \times x}}$
Using the above rule, we will solve the question.
So,
${\left( {xy{z^2}} \right)^4} = {x^4} \times {y^4} \times {z^8}$
First term can be written as:-
${\left( x \right)^4} = {x^4}$
Second term can be written as:-
${\left( y \right)^4} = {y^4}$
Third term can be written as:-
${\left( {{z^2}} \right)^4} = {z^{2 \times 4}} \\\ \Rightarrow{\left( {{z^2}} \right)^4}= {z^8} \\\$
Now, replacing the terms in the question we will get:-
${\left( {xy{z^2}} \right)^4} = {x^4} \times {y^4} \times {z^8}$

Hence, ${x^4} \times {y^4} \times {z^8}$ is the most simplified form of the given ${\left( {xy{z^2}} \right)^4}$ form.

Note: Simplification of the first two terms is very easy as all you have to do is write the power over the variable itself. But for the term “z”, you need to multiply the power inside and outside. Don’t add the powers as it will give you wrong answers. Addition of powers is done in cases when two numbers with the same base with same or different powers are added.