Question

How do you simplify \[{{\left( 4zy \right)}^{-1}}\] and write it using only positive exponents?

Answer 1

Hint: In the above question we are asked to write the given expression in terms of positive exponent. This means the power or the index of the given expression should be positive. Therefore, we will use simple exponential rules in order to rewrite the expression in terms of positive exponents.

Complete step by step answer: The concept used in the above question is conversion of negative exponents into positive. In an exponential expression we have two terminologies one is base and the other is index or power. Let us take an example. Consider an exponential expression \[{{a}^{3}}\] , here \[a\] is the base whose value is known and 3 is the power or the index to which the base is raised. If the value of the power is positive then it is called a positive exponent and if the power is negative then it is called a negative exponent.
In order to convert a negative exponent expression into positive exponent we will rewrite the expression using the identity \[{{\left( y \right)}^{-1}}=\dfrac{1}{y}\] .
Now in the question we have \[{{\left( 4zy \right)}^{-1}}\] . Here we can see that the negative exponent is on the whole expression. Therefore, we will use the above-mentioned identity.
Rewriting the given expression.
\[{{\left( 4zy \right)}^{-1}}=\dfrac{1}{4zy}\]
Hence, the answer for the given expression is \[\dfrac{1}{4zy}\] .

Note:Be careful while solving these types of questions. While solving the above question keep in mind the basic exponential rules. Before converting the expression into a negative exponent, check whether the sign is over the whole expression or not. Try to perform each and every step.