Question

Simplify the following expression. Assume x>0 and write your answer without radicals.(169x)1/2⋅(4x−6/7)

Answer 1

The answer is

`52x^{-(5)/(14)}`

SOLUTION

Problem Statement

We are given the following expression to evaluate:

`(169x)^{(1)/(2)}\text{.}(4x^{-(6)/(7)})`

Method

- To solve this question, we need to know some laws of indices. These laws are given below:

`\begin{gathered} \text{ Law 1:} \\ a^b* a^c=a^(b+c) \\ \\ \text{Law 2:} \\ (ab)^c=a^c* b^c \end{gathered}`

Implementation

Let us apply the law above to solve the question as follows:

`\begin{gathered} (169x)^{(1)/(2)}\text{.}4x^{-(6)/(7)}) \\ By\text{ Law 2, we have:} \\ =169^{(1)/(2)}* x^{(1)/(2)}*4* x^{-(6)/(7)} \\ \\ But\text{ }169^{(1)/(2)}=\sqrt[]{169}=13 \\ 169^{(1)/(2)}* x^{(1)/(2)}*4* x^{-(6)/(7)}=13* x^{(1)/(2)}*4* x^{-(6)/(7)} \\ \\ Collect\text{ like terms} \\ 13*4* x^{(1)/(2)}* x^{-(6)/(7)}=52* x^{(1)/(2)}* x^{-(6)/(7)} \\ \\ By\text{ Law 1, we have:} \\ x^{(1)/(2)}* x^{-(6)/(7)}=x^{(1)/(2)-(6)/(7)}=x^{-(5)/(14)} \\ \\ \therefore52* x^{(1)/(2)}* x^{-(6)/(7)}=52* x^{-(5)/(14)} \end{gathered}`

Final Answer

The answer is

`52x^{-(5)/(14)}`