\( \begin{array}{ll}\text { 7. } \sqrt{\frac{25}{36}} r^{2} t & \text { 8. } \sqrt{\frac{192 k^{4}}{64}} \\ \sqrt[5]{\frac{3072 h^{3}}{243 f^{8}}} & \text { 10. } \sqrt[3]{\frac{432 n^{12}}{64 q^{6}}}\end{array} \)

Simplify the expression by following steps: - step0: Solution: \(\sqrt{\frac{25}{36}}\times r^{2}t\) - step1: Simplify the root: \(\frac{5}{6}r^{2}t\) Calculate or simplify the expression \( \sqrt(192 * k^4 / 64) \). Simplify the expression by following steps: - step0: Solution: \(\sqrt{\frac{192k^{4}}{64}}\) - step1: Divide the terms: \(\sqrt{3k^{4}}\) - step2: Reorder the terms: \(\sqrt{k^{4}\times 3}\) - step3: Use the properties of radicals: \(\sqrt{k^{4}}\times \sqrt{3}\) - step4: Simplify the root: \(\sqrt{3}\times k^{2}\) Calculate or simplify the expression \( (432 * n^12 / 64 * q^6)^(1/3) \). Simplify the expression by following steps: - step0: Solution: \(\left(\frac{432n^{12}}{64}q^{6}\right)^{\frac{1}{3}}\) - step1: Reduce the fraction: \(\left(\frac{27n^{12}}{4}q^{6}\right)^{\frac{1}{3}}\) - step2: Multiply the terms: \(\left(\frac{27n^{12}q^{6}}{4}\right)^{\frac{1}{3}}\) - step3: Rewrite the expression: \(\frac{\left(27n^{12}q^{6}\right)^{\frac{1}{3}}}{4^{\frac{1}{3}}}\) - step4: Evaluate the power: \(\frac{3n^{4}q^{2}}{\sqrt[3]{4}}\) - step5: Simplify: \(\frac{3\sqrt[3]{4^{2}}\times n^{4}q^{2}}{2^{2}}\) - step6: Evaluate the power: \(\frac{3\sqrt[3]{16}\times n^{4}q^{2}}{4}\) Calculate or simplify the expression \( (3072 * h^3 / 243 * f^8)^(1/5) \). Simplify the expression by following steps: - step0: Solution: \(\left(\frac{3072h^{3}}{243}f^{8}\right)^{\frac{1}{5}}\) - step1: Reduce the fraction: \(\left(\frac{1024h^{3}}{81}f^{8}\right)^{\frac{1}{5}}\) - step2: Multiply the terms: \(\left(\frac{1024h^{3}f^{8}}{81}\right)^{\frac{1}{5}}\) - step3: Rewrite the expression: \(\frac{\left(1024h^{3}f^{8}\right)^{\frac{1}{5}}}{81^{\frac{1}{5}}}\) - step4: Evaluate the power: \(\frac{4h^{\frac{3}{5}}f^{\frac{8}{5}}}{\sqrt[5]{81}}\) - step5: Simplify: \(\frac{4f\sqrt[5]{h^{3}f^{3}}}{\sqrt[5]{81}}\) - step6: Calculate: \(\frac{4f\sqrt[5]{3f^{3}h^{3}}}{3}\) Here are the simplified results for each expression: 7. For \( \sqrt{\frac{25}{36}} r^{2} t \): \[ \frac{5}{6} r^{2} t \] 8. For \( \sqrt{\frac{192 k^{4}}{64}} \): \[ \sqrt{3} \times k^{2} \] 9. For \( \sqrt[5]{\frac{3072 h^{3}}{243 f^{8}}} \): \[ \frac{4f\sqrt[5]{3f^{3}h^{3}}}{3} \] 10. For \( \sqrt[3]{\frac{432 n^{12}}{64 q^{6}}} \): \[ \frac{3\sqrt[3]{16} \times n^{4} q^{2}}{4} \] These results provide the simplified forms of the given expressions.