Explanation:
Question 2
To answer the question, we will use the exponential laws
[tex]\begin{gathered} a^{\frac{1}{b}}=\sqrt[b]{a} \\ a^{-1}=\frac{1}{a} \\ a^{\frac{b}{c}}=\sqrt[c]{a^b} \\ a^b\times a^c=a^{b+c} \\ a^b\div a^c=a^{b-c} \end{gathered}[/tex]
Applying these laws
Question 2a
[tex]\sqrt[4]{(mn)^{12}}=(mn)^{\frac{12}{4}}[/tex][tex]\sqrt[4]{(mn)^{12}}=(mn)^{\frac{12}{4}}=(mn)^3[/tex]
Question 2b
[tex]\sqrt{x}.\sqrt[7]{x}[/tex]
we will rewrite it as
[tex]x^{\frac{1}{2}}\times x^{\frac{1}{7}}=x^{\frac{1}{2}+\frac{1}{7}}=x^{\frac{9}{14}}[/tex]
Question 2c
[tex]\frac{\sqrt[6]{x}}{\sqrt[4]{x}}=\frac{x^{\frac{1}{6}}}{x^{\frac{1}{4}}}[/tex]
Then
[tex]\frac{x^{\frac{1}{6}}}{x^{\frac{1}{4}}}=x^{\frac{1}{6}-\frac{1}{4}}=x^{-\frac{1}{12}}=\frac{1}{x^{12}}[/tex]
Question 2d
[tex]\sqrt[6]{\frac{r^6}{s^{18}}}=(\frac{r^6}{s^{18}})^{\frac{1}{6}}[/tex]
Simplifying further
[tex]\frac{r^{\frac{6}{6}}}{s^{\frac{18}{6}}}=\frac{r}{s^3}[/tex]
Question 2e
[tex]\sqrt[3]{x^6q^9}=(x^6q^9)^{\frac{1}{3}}[/tex]
Simplifying further
[tex](x^6q^9)^{\frac{1}{3}}=x^{\frac{6}{3}}q^{\frac{9}{3}}=x^2q^3[/tex]
Question 2f
[tex]\sqrt{49x^5}=(49x^5)^{\frac{1}{2}}[/tex]
Simplifying further
[tex]49^{\frac{1}{2}}x^{\frac{5}{2}}=7x^{\frac{5}{2}}[/tex]
