Answer:
Option (3)
Step-by-step explanation:
Given expression is,
[tex]\frac{2^3\times 125^\frac{2}{3}\times 81^\frac{3}{4}}{8^\frac{1}{3}\times 9\times 5^2}[/tex]
To solve the given expression we will apply the law of exponents,
[tex]\frac{2^3\times 125^\frac{2}{3}\times 81^\frac{3}{4}}{8^\frac{1}{3}\times 9\times 5^2}=\frac{2^3\times (5^3)^\frac{2}{3}\times (3^4)^\frac{3}{4}}{(2^3)^\frac{1}{3}\times (3^2)\times 5^2}[/tex]
[tex]=\frac{2^3\times (5^{3\times \frac{2}{3}})\times (3^{4\times \frac{3}{4}})}{(2^{3\times \frac{1}{3}})\times (3^2)\times 5^2}[/tex]
[tex]=\frac{2^3\times 5^2\times 3^3}{2\times 3^2\times 5^2}[/tex]
[tex]=\frac{2^3}{2}\times (\frac{5^2}{5^2})\times (\frac{3^3}{3^2})[/tex]
[tex]=2^{3-1}\times (1)\times 3^{3-2}[/tex]
[tex]=2^2\times 1\times 3[/tex]
[tex]=12[/tex]
Therefore, Option (3) will be the correct option.
