![\bf a^{\frac{{ n}}{{ m}}} \implies \sqrt[{ m}]{a^{ n}} \qquad \qquad \sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}\\\\ -----------------------------\\\\ 7^{\frac{19}{4}}\cdot \sqrt[a]{7^b}=7^{\frac{9}{4}}\cdot \sqrt{7^3}\implies 7^{\frac{19}{4}}\cdot \sqrt[a]{7^b}=7^{\frac{9}{4}}\cdot \sqrt[2]{7^3} \\\\\\ 7^{\cfrac{}{}\frac{19}{4}}\cdot 7^{\cfrac{}{}\frac{b}{a}}=7^{\cfrac{}{}\frac{9}{4}}\cdot 7^{\cfrac{}{}\frac{3}{2}}\implies 7^{\cfrac{}{}\frac{19}{4}+\frac{b}{a}}=7^{\cfrac{}{}\frac{9}{4}+\frac{3}{2}}](/tpl/images/0477/0212/eb9bf.png)
What are the possible values of a and b?
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