The simplification will give;
[tex]\frac{7\sqrt[]{q^9r^7}}{2}[/tex]
Here, we want to make a simplification
We proceed as follows;
[tex]\sqrt[]{\frac{49q^9r^7}{4}}\text{ = }\frac{\sqrt[]{49}\text{ }\times\sqrt[]{q^9\text{ }}\text{ }\times\sqrt[]{r^7}}{\sqrt[]{4}}[/tex]
As we can see, the power of 9 and 7 are not perfect squares since they are odd
Thus, we have the expression as;
[tex]\frac{7\times\sqrt[]{q^{9\text{ }}}\text{ }\times\sqrt[]{r^7}}{2}\text{ = }\frac{7\sqrt[]{q^9r^7}}{2}[/tex]
According to laws of indices;
[tex]\begin{gathered} a^9=a^{4.5}\times a^{4.5} \\ a^6=a^3\times a^3 \\ (a^9)^{\frac{1}{2}}=a^{\frac{9}{2}} \\ (a^6)^{\frac{1}{2}}=a^{\frac{6}{2}}=a^3 \end{gathered}[/tex]
