Recall that, when two terms are being multiplied and they have the same number we can add the exponents:
[tex]x^nx^m=x^{n+m}.[/tex]
Applying the above property to the given expressions, we get:
[tex]\begin{gathered} 6^{\frac{9}{5}}6^{\frac{1}{5}}=6^{\frac{9}{5}+\frac{1}{5}}, \\ x^{\frac{10}{3}}x^{\frac{11}{3}}=x^{\frac{10}{3}+\frac{11}{3}}, \\ y^{\frac{7}{2}}y^{\frac{1}{2}}=y^{\frac{7}{2}+\frac{1}{2}}. \end{gathered}[/tex]
Simplifying the above results, we get:
[tex]\begin{gathered} 6^{\frac{9}{5}}6^{\frac{1}{5}}=6^2, \\ x^{\frac{10}{3}}x^{\frac{11}{3}}=x^7, \\ y^{\frac{7}{2}}y^{\frac{1}{2}}=y^4. \end{gathered}[/tex]
Answer:
[tex]\begin{gathered} 6^{\frac{9}{5}}6^{\frac{1}{5}}=6^2, \\ x^{\frac{10}{3}}x^{\frac{11}{3}}=x^7, \\ y^{\frac{7}{2}}y^{\frac{1}{2}}=y^4. \end{gathered}[/tex]
