How do you simplify \[9{{x}^{\dfrac{1}{5}}}-2{{x}^{\dfrac{1}{5}}}\] ?

Hint: We have been given an expression which consists of two exponential terms as the x-variable has been assigned a fractional power. Here, we shall notice that both the terms consist of the x-variable which has the same power. Thus, we can take this x-variable common and perform the mathematical operation on the remaining terms. After subtracting the remaining constant terms, we will obtain the simplest form of the given expression.

Complete step by step solution:
Given that \[9{{x}^{\dfrac{1}{5}}}-2{{x}^{\dfrac{1}{5}}}\].
We know that while simplifying mathematical expressions and equations, only like terms are taken common which consist of the same variables or same constants raised to same powers.
Here in both the terms of the expression \[9{{x}^{\dfrac{1}{5}}}-2{{x}^{\dfrac{1}{5}}}\], ${{x}^{\dfrac{1}{5}}}$ is occurring. Thus, we shall take it common and get
\[\Rightarrow 9{{x}^{\dfrac{1}{5}}}-2{{x}^{\dfrac{1}{5}}}=\left( 9-2 \right){{x}^{\dfrac{1}{5}}}\]
Now, we will subtract the integers remaining in the bracket. Subtracting 2 from 9, we get
\[\Rightarrow 9{{x}^{\dfrac{1}{5}}}-2{{x}^{\dfrac{1}{5}}}=7{{x}^{\dfrac{1}{5}}}\]

Therefore, the given expression \[9{{x}^{\dfrac{1}{5}}}-2{{x}^{\dfrac{1}{5}}}\] is simplified to \[7{{x}^{\dfrac{1}{5}}}\] by using simple grouping method of algebraic terms.

Note: We must remember that if the same power would not have been assigned to the x-variable in both the terms, then we would have taken the x-variable common which would be assigned the smaller power of the two powers. Then, the x-variable term with the larger power would be modified as the smaller power would have been subtracted from the larger one. This is because taking a term common is similar to multiplying and dividing the entire expression with that term.