Ответ:

[tex]\frac{2^{4}}{3}=\frac{16}{3}=5\frac{1}{3}[/tex].

Объяснение:

[tex]a^{b}\cdot a^{c}=a^{b+c}\\\\\frac{a^{b}}{a^{c}}=a^{b-c}\\\\(a^{b})^{c}=a^{b\cdot c}=(a^{c})^{b}[/tex]

[tex]\frac{(0,5)^{3}\cdot8^{7}\cdot12^{2}}{6^{3}\cdot2^{15}}=(\frac{1}{2})^{3}\cdot\frac{(2^{3})^{7}\cdot(2\cdot2\cdot3)^{2}}{(2\cdot3)^{3}\cdot2^{15}}=\frac{1^{3}\cdot2^{21}\cdot2^{4}\cdot3^{2}}{2^{3}\cdot2^{3}\cdot3^{3}\cdot2^{15}}=\frac{2^{25}\cdot3^{2}}{2^{21}\cdot3^{3}}=\frac{2^4}{3^1}=\frac{2^{4}}{3}=\frac{16}{3}=5\frac{1}{3}[/tex]