Thực hiện tính \(\frac{{{{10}^{500}} \cdot {5^{1515}}}}{{{{25}^{1008}} \cdot {8^{166}}}}\)

* Hướng dẫn giải

Ta có:  \(\frac{{{{10}^{500}} \cdot {5^{1515}}}}{{{{25}^{1008}} \cdot {8^{166}}}} = \frac{{{{\left( {2.5} \right)}^{500}} \cdot {5^{1515}}}}{{{{\left( {{5^2}} \right)}^{1008}} \cdot {{\left( {{2^3}} \right)}^{166}}}} = \frac{{{2^{500}}{{.5}^{500}}{{.5}^{1515}}}}{{{5^{2016}}{{.2}^{498}}}} = \frac{{{2^{500}}{{.5}^{2015}}}}{{{5^{2016}}{{.2}^{498}}}} = \frac{{{2^2}}}{5} = \frac{4}{5}\)