Question

What is the simplified expression​

Answer 1

`\rightarrow (4^(-3) * 3^(4) * 4^(2) )/(3^(5) * 4^(-2) )`

`\rightarrow 4^(-3 + 2) * 3^(4 - 5) * 4^(2) }`

`\rightarrow 4^(-1) * 3^(-1) * 16}`

`\rightarrow (1)/(4) * (1)/(3) * 16}`

`\rightarrow (1)/(12) * 16}`

`\rightarrow (16)/(12)`

`\rightarrow \boxed{\bold{(4)/(3) \tex\text{ (Option B)}}}`

Answer 2

`\frac43`

Explanation:

`(4^(-3)\cdot3^4\cdot4^2)/(3^5\cdot4^(-2))`

Separate like terms:

`\implies (4^(-3)\cdot4^2)/(4^(-2))\cdot (3^4)/(3^5)`

Use exponent rule
`a^b \cdot a^c=a^((b+c))` :

`\implies (4^((-3+2)))/(4^(-2))\cdot (3^4)/(3^5)`

`\implies (4^(-1))/(4^(-2))\cdot (3^4)/(3^5)`

Use exponent rule
`(a^b)/(a^c)=a^((b-c))`

`\implies 4^((-1--2))\cdot {3^((4-5))`

`\implies 4^(1)\cdot {3^(-1)`

Use exponent rule
`a^(-1)=(1)/(a)`

`\implies 4\cdot \frac13`

`\implies \frac43`