3^5/6^3 * 4^7/8
You asked:
Evaluate the expression: \(\frac{\frac{{3}^{5}}{{6}^{3}} \cdot {4}^{7}}{8}\)
MathBot Answer:
\[\frac{\frac{{3}^{5}}{{6}^{3}} \cdot {4}^{7}}{8} = 2304\]
\[\begin{aligned}\frac{\frac{{3}^{5}}{{6}^{3}} \cdot {4}^{7}}{8}& = 3^{5} \cdot \frac{1}{6^{3}} \cdot 4^{7} \cdot \frac{1}{8}\\& = 243 \cdot \frac{1}{6^{3}} \cdot 4^{7} \cdot \frac{1}{8}\\& = \frac{243}{216} \cdot 4^{7} \cdot \frac{1}{8}\\& = \frac{243}{216} \cdot \frac{16384}{8}\\& = \frac{243}{216} \cdot 2048\\& = \frac{9}{8} \cdot 2048\\& = 2304\end{aligned}\]