Question

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

Answer 1

Answer

The answer is

$52x^{-\frac{5}{14}}$

SOLUTION

Problem Statement

We are given the following expression to evaluate:

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

Method

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

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

Implementation

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

$\begin{gathered} (169x)^{\frac{1}{2}}\text{.}4x^{-\frac{6}{7}}) \\ By\text{ Law 2, we have:} \\ =169^{\frac{1}{2}}\times x^{\frac{1}{2}}\times4\times x^{-\frac{6}{7}} \\ \\ But\text{ }169^{\frac{1}{2}}=\sqrt[]{169}=13 \\ 169^{\frac{1}{2}}\times x^{\frac{1}{2}}\times4\times x^{-\frac{6}{7}}=13\times x^{\frac{1}{2}}\times4\times x^{-\frac{6}{7}} \\ \\ Collect\text{ like terms} \\ 13\times4\times x^{\frac{1}{2}}\times x^{-\frac{6}{7}}=52\times x^{\frac{1}{2}}\times x^{-\frac{6}{7}} \\ \\ By\text{ Law 1, we have:} \\ x^{\frac{1}{2}}\times x^{-\frac{6}{7}}=x^{\frac{1}{2}-\frac{6}{7}}=x^{-\frac{5}{14}} \\ \\ \therefore52\times x^{\frac{1}{2}}\times x^{-\frac{6}{7}}=52\times x^{-\frac{5}{14}} \end{gathered}$

Final Answer

The answer is

$52x^{-\frac{5}{14}}$