\frac{(3 {a}^(2) )(4 {b}^(3) )}{16( {a}^(2)b) {}^(2) } =Simplify this fraction

Question

`\frac{(3 {a}^(2) )(4 {b}^(3) )}{16( {a}^(2)b) {}^(2) } =`Simplify this fraction

Answer 1

We can multiply the terms of top, then we have

`((3a^2)(4b^3))/(16(a^2b)^2)=(12a^2b^3)/(16(a^2b)^2)`

now, in the denominator, we have

`16(a^2b)^2=16a^(2\cdot2)b^2=16a^4b^2`

then, we obtain

`((3a^2)(4b^3))/(16(a^2b)^2)=\frac{12a^2b^3}{16a^4b^2^{}}`

Now, we can see that

`(12)/(16)=(4\cdot3)/(4\cdot4)=(3)/(4)`

and

`(a^2)/(a^4)=(a^2)/(a^2\cdot a^2)=(1)/(a^2)`

and also

`(b^3)/(b^2)=(b^2\cdot b)/(b^2)=b`

by combaning these results, the answer is

`((3a^2)(4b^3))/(16(a^2b)^2)=\frac{3b}{4a^2^{}}`