Question

Simplify$\frac{{\left(-4m^{-3}\right)}^2{\left(5m^4\right)}^3}{{\left(-10m^6\right)}^3}$

Short answer

Simplified expression is$-2m^{-12}$

Step-by-step solution

Given information  

Simplify$\frac{{\left(-4m^{-3}\right)}^2{\left(5m^4\right)}^3}{{\left(-10m^6\right)}^3}$

Simplification

Here

$$\begin{gathered} \frac{{\left(-4m^{-3}\right)}^2{\left(5m^4\right)}^3}{{\left(-10m^6\right)}^3}=\frac{{\left(-4\right)}^2{\left(m^{-3}\right)}^2{\left(5\right)}^3{\left(m^4\right)}^3}{{\left(-10\right)}^3{\left(m^6\right)}^3} \\ =\frac{16m^{-6}\times 125m^{12}}{-1000m^{18}} \\ =-2m^{-6+12-18} \\ =-2m^{-12} \end{gathered}$$