(2^2*3^3*5^7)/(2^3*3^4*5^6)

asked by guest
on Jan 23, 2025 at 11:10 pm



You asked:

Evaluate the expression: \(\frac{{2}^{2} \cdot {3}^{3} \cdot {5}^{7}}{{2}^{3} \cdot {3}^{4} \cdot {5}^{6}}\)

MathBot Answer:

\[\frac{{2}^{2} \cdot {3}^{3} \cdot {5}^{7}}{{2}^{3} \cdot {3}^{4} \cdot {5}^{6}} = \frac{5}{6} = 0.8\overline{3}\]

\[\begin{aligned}\frac{{2}^{2} \cdot {3}^{3} \cdot {5}^{7}}{{2}^{3} \cdot {3}^{4} \cdot {5}^{6}}& = 2^{2} \cdot 3^{3} \cdot 5^{7} \cdot \frac{1}{2^{3} \cdot 3^{4} \cdot 5^{6}}\\& = 4 \cdot 3^{3} \cdot 5^{7} \cdot \frac{1}{2^{3} \cdot 3^{4} \cdot 5^{6}}\\& = 4 \cdot 27 \cdot 5^{7} \cdot \frac{1}{2^{3} \cdot 3^{4} \cdot 5^{6}}\\& = 4 \cdot 27 \cdot 78125 \cdot \frac{1}{2^{3} \cdot 3^{4} \cdot 5^{6}}\\& = 4 \cdot 27 \cdot 78125 \cdot \frac{1}{8 \cdot 3^{4} \cdot 5^{6}}\\& = 4 \cdot 27 \cdot 78125 \cdot \frac{1}{8 \cdot 81 \cdot 5^{6}}\\& = 4 \cdot 27 \cdot 78125 \cdot \frac{1}{8 \cdot 81 \cdot 15625}\\& = 4 \cdot 27 \cdot 78125 \cdot \frac{1}{648 \cdot 15625}\\& = 4 \cdot 27 \cdot \frac{78125}{10125000}\\& = 4 \cdot 27 \cdot \frac{5}{648}\\& = 108 \cdot \frac{5}{648}\\& = \frac{5}{6}\end{aligned}\]

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