Warum kommt bei (7/32)^4*8^4 gleich 2401/256 raus? (Rechenweg)

$${\left({\frac{{\mathtt{7}}}{{\mathtt{32}}}}\right)}^{{\mathtt{4}}} = {\mathtt{0.002\: \!289\: \!772\: \!033\: \!691\: \!4}}$$        ;       $${{\mathtt{8}}}^{{\mathtt{4}}} = {\mathtt{4\,096}}$$

$${\left({\frac{{\mathtt{7}}}{{\mathtt{32}}}}\right)}^{{\mathtt{4}}}{\mathtt{\,\times\,}}{{\mathtt{8}}}^{{\mathtt{4}}} = {\frac{{\mathtt{2\,401}}}{{\mathtt{256}}}} = {\mathtt{9.378\: \!906\: \!25}}$$

$${\left({\frac{\left({\mathtt{7}}{\mathtt{\,\times\,}}{\mathtt{8}}\right)}{{\mathtt{32}}}}\right)}^{{\mathtt{4}}} = {\frac{{\mathtt{2\,401}}}{{\mathtt{256}}}} = {\mathtt{9.378\: \!906\: \!25}}$$        =     $${\left({\frac{{\mathtt{7}}}{{\mathtt{4}}}}\right)}^{{\mathtt{4}}} = {\frac{{\mathtt{2\,401}}}{{\mathtt{256}}}} = {\mathtt{9.378\: \!906\: \!25}}$$

$${\frac{{{\mathtt{7}}}^{{\mathtt{4}}}}{{{\mathtt{4}}}^{{\mathtt{4}}}}} = {\frac{{\mathtt{2\,401}}}{{\mathtt{256}}}} = {\mathtt{9.378\: \!906\: \!25}}$$

Man kann die Potenzen mit gleichem Exponenten zusammenfassen und in der Klammer kann dann durch 8 gekürzt werden.

Gruß radix !