<s>[INST] Simplify $\frac{7^{ \log_{5} 15 }+3^{2+\log_{5}7}}{7^{\log_{5}3}}$ I know that the result of this expression is 16 but how do I get to that result?
$$\frac{7^{ \log_{5} 15    }+3^{2+\log_{5}7}}{7^{\log_{5}3}}$$
 [/INST] $$\frac{7^{ \log_{5} 15    }+3^{2+\log_{5}7}}{7^{\log_{5}3}}=\frac{7^{ 1+\log_53    }+7^{\left(2+\log_{5}7\right)\log_73}}{7^{\log_{5}3}}=7+\frac{7^{\log_79+\log_53}}{7^{\log_53}}=7+9=16.$$
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