Question

What is the simplified expression for

Answer 1

The simplified expression for
`(3^(-4) * 2^(3) * 3^(2))/(2^(4) * 3^(-3))` is
`(3)/(2)`

Solution:

The given equation is
`(3^(-4) * 2^(3) * 3^(2))/(2^(4) * 3^(-3))`

Simplifying the equation we get,

`(3^(-4) * 2^(3) * 3^(2))/(2^(4) * 3^(-3))`

`\Rightarrow (\left(3^(-4) * 3^(2)\right) * 2^(3))/(2^(4) * 3^(-3))`

Simplifying the exponential form,

`\Rightarrow (3^(-4+2) * 2^(3))/(2^(4) * 3^(-3))`

`\Rightarrow (3^(-2) * 2^(3))/(2^(4) * 3^(-3))`

`\Rightarrow\left((3^(-2))/(3^(-3))\right) *\left((2^(3))/(2^(4))\right)`

`\Rightarrow 3^(-2+3) * 2^(3-4)`

`\Rightarrow 3^(1) * 2^(-1)`

On simplifying the exponential form we get,

`\Rightarrow (3)/(2)`