Q. 161 - Intermediate Algebra

Question

Simplify $\frac{{\left(-10n^{-2}\right)}^3{\left(4n^5\right)}^2}{{\left(2n^8\right)}^2}$

Step-by-Step Solution

Answer

Simplified expression is$-4000n^{-12}$

Step 1 Given information

Simplify$\frac{{\left(-10n^{-2}\right)}^3{\left(4n^5\right)}^2}{{\left(2n^8\right)}^2}$

Step 2 Simplification

Here

$$\begin{gathered} \frac{{\left(-10n^{-2}\right)}^3{\left(4n^5\right)}^2}{{\left(2n^8\right)}^2}=\frac{{\left(-10\right)}^3{\left(n^{-2}\right)}^3{\left(4\right)}^2{\left(n^5\right)}^2}{{\left(2\right)}^2{\left(n^8\right)}^2} \\ =\frac{-1000\times n^{-6}\times 16\times n^{10}}{4\times n^{16}} \\ =-4000n^{-6+10-16} \\ =-4000n^{-12} \end{gathered}$$