Question

Express the algebraic expression $\frac{16{\mathrm{x}}^2{\mathrm{y}}^2}{24{\mathrm{xy}}^3}$in its lowest form.

Answer 1

To simplify : $\frac{16{\mathrm{x}}^2{\mathrm{y}}^2}{24{\mathrm{xy}}^3}$

Prime factor of $16{\mathrm{x}}^2{\mathrm{y}}^2=2\times 2\times 2\times 2\times \mathrm{x}\times \mathrm{x}\times \mathrm{y}\times \mathrm{y}$

Prime factor of $24{\mathrm{xy}}^3=2\times 2\times 2\times 3\times \mathrm{x}\times \mathrm{y}\times \mathrm{y}\times \mathrm{y}$

H.C.F of $16{\mathrm{x}}^2{\mathrm{y}}^2$ and $24{\mathrm{xy}}^3$$=8{\mathrm{xy}}^2$

Dividing numerator and denominator of $\frac{16{\mathrm{x}}^2{\mathrm{y}}^2}{24{\mathrm{xy}}^3}$ by the H.C.F obtained , we get

$\frac{16{\mathrm{x}}^2{\mathrm{y}}^2}{24{\mathrm{xy}}^3}=\frac{16{\mathrm{x}}^2{\mathrm{y}}^2÷8{\mathrm{xy}}^2}{24{\mathrm{xy}}^3÷8{\mathrm{xy}}^2}$

$=\frac{{\displaystyle \frac{16\times \mathrm{x}\times \mathrm{x}\times \mathrm{y}\times \mathrm{y}}{8\times \mathrm{x}\times \mathrm{y}\times \mathrm{y}}}}{{\displaystyle \frac{24\times x\times \mathrm{y}\times \mathrm{y}\times \mathrm{y}}{8\times \mathrm{x}\times \mathrm{y}\times \mathrm{y}}}}$

$=\frac{{\displaystyle \frac{2\times 1\times \mathrm{x}\times 1\times 1}{1\times 1\times 1\times 1}}}{{\displaystyle \frac{3\times 1\times \mathrm{y}\times 1\times 1}{1\times 1\times 1\times 1}}}$

$=2\mathrm{x}\times \frac{1}{3\mathrm{y}}$

$=\frac{2\mathrm{x}}{3\mathrm{y}}$

Thus ,$\frac{16{\mathrm{x}}^2{\mathrm{y}}^2}{24{\mathrm{xy}}^3}$$=\frac{2\mathrm{x}}{3\mathrm{y}}$ Answer