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

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

now, in the denominator, we have

$16(a^2b)^2=16a^{2\cdot2}b^2=16a^4b^2$

then, we obtain

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

Now, we can see that

$\frac{12}{16}=\frac{4\cdot3}{4\cdot4}=\frac{3}{4}$

and

$\frac{a^2}{a^4}=\frac{a^2}{a^2\cdot a^2}=\frac{1}{a^2}$

and also

$\frac{b^3}{b^2}=\frac{b^2\cdot b}{b^2}=b$

by combaning these results, the answer is

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