Question

Simplify$\frac{9{\mathrm{m}}^4}{18{\mathrm{mn}}^3}$

Short answer

Simplified answer is$\frac{{\mathrm{m}}^3}{2{\mathrm{n}}^3}.$

Step-by-step solution

Step 1. Given Data

Given expression is$\frac{9{\mathrm{m}}^4}{18{\mathrm{mn}}^3}.$

Step 2. Factorization

On Factorizing,

$=\frac{9.\mathrm{m}.{\mathrm{m}}^3}{9.2.\mathrm{m}.{\mathrm{n}}^3}$

On dividing out the common factor and simplify,

$$\begin{gathered} =\frac{{\mathrm{m}}^3}{2.{\mathrm{n}}^3} \\ =\frac{{\mathrm{m}}^3}{2{\mathrm{n}}^3} \end{gathered}$$

The simplified expression is$\frac{{\mathbf{m}}^{\mathbf{3}}}{\mathbf{2}{\mathbf{n}}^{\mathbf{3}}}.$