(3^6*(2)^5*5^2)/(9^3*4^3*5)

asked by guest
on Oct 21, 2024 at 10:26 pm



You asked:

Evaluate the expression: \(\frac{{3}^{6} \cdot {2}^{5} \cdot {5}^{2}}{{9}^{3} \cdot {4}^{3} \cdot 5}\)

MathBot Answer:

\[\frac{{3}^{6} \cdot {2}^{5} \cdot {5}^{2}}{{9}^{3} \cdot {4}^{3} \cdot 5} = \frac{5}{2} = 2.5\]

\[\begin{aligned}\frac{{3}^{6} \cdot {2}^{5} \cdot {5}^{2}}{{9}^{3} \cdot {4}^{3} \cdot 5}& = 3^{6} \cdot 2^{5} \cdot 5^{2} \cdot \frac{1}{9^{3} \cdot 4^{3} \cdot 5}\\& = 729 \cdot 2^{5} \cdot 5^{2} \cdot \frac{1}{9^{3} \cdot 4^{3} \cdot 5}\\& = 729 \cdot 32 \cdot 5^{2} \cdot \frac{1}{9^{3} \cdot 4^{3} \cdot 5}\\& = 729 \cdot 32 \cdot 25 \cdot \frac{1}{9^{3} \cdot 4^{3} \cdot 5}\\& = 729 \cdot 32 \cdot 25 \cdot \frac{1}{729 \cdot 4^{3} \cdot 5}\\& = 729 \cdot 32 \cdot 25 \cdot \frac{1}{729 \cdot 64 \cdot 5}\\& = 729 \cdot 32 \cdot 25 \cdot \frac{1}{46656 \cdot 5}\\& = 729 \cdot 32 \cdot \frac{25}{233280}\\& = 729 \cdot 32 \cdot \frac{5}{46656}\\& = 23328 \cdot \frac{5}{46656}\\& = \frac{5}{2}\end{aligned}\]

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