Answer:
The simplified expression for[tex]\frac{3^{-4} \times 2^{3} \times 3^{2}}{2^{4} \times 3^{-3}}[/tex] is [tex]\frac{3}{2}[/tex]
Solution:
The given equation is [tex]\frac{3^{-4} \times 2^{3} \times 3^{2}}{2^{4} \times 3^{-3}}[/tex]
Simplifying the equation we get,
[tex]\frac{3^{-4} \times 2^{3} \times 3^{2}}{2^{4} \times 3^{-3}}[/tex]
[tex]\Rightarrow \frac{\left(3^{-4} \times 3^{2}\right) \times 2^{3}}{2^{4} \times 3^{-3}}[/tex]
Simplifying the exponential form,
[tex]\Rightarrow \frac{3^{-4+2} \times 2^{3}}{2^{4} \times 3^{-3}}[/tex]
[tex]\Rightarrow \frac{3^{-2} \times 2^{3}}{2^{4} \times 3^{-3}}[/tex]
[tex]\Rightarrow\left(\frac{3^{-2}}{3^{-3}}\right) \times\left(\frac{2^{3}}{2^{4}}\right)[/tex]
[tex]\Rightarrow 3^{-2+3} \times 2^{3-4}[/tex]
[tex]\Rightarrow 3^{1} \times 2^{-1}[/tex]
On simplifying the exponential form we get,
[tex]\Rightarrow \frac{3}{2}[/tex]
