Home » » Simplify $$\left(\frac{8\sqrt n^2}{m^{3/2}}\right)\left(\frac{4^{-1}m^2}{2n^{-2}}\right)$$...

# Simplify $$\left(\frac{8\sqrt n^2}{m^{3/2}}\right)\left(\frac{4^{-1}m^2}{2n^{-2}}\right)$$...

### Question

Simplify $$\left(\frac{8\sqrt n^2}{m^{3/2}}\right)\left(\frac{4^{-1}m^2}{2n^{-2}}\right)$$

### Options

A) $$128n^3m^{-1}$$

B) $$8n^3m^{-1}$$

C) $$8n^3m$$

D) $$8n^4m$$

### Explanation:

$$\left[\frac{\sqrt[8]n}{m^{\frac 3 2}}\right]^2\left[\frac{4^{-1}m^2}{2n^{-2}}\right]=(8\sqrt n)^2$$
$$\frac{64n}{m^3} \times \frac{\frac 1 4 \times m^2}{2 \times \frac 1{n^2}}$$
$$\frac{64n}{m^3} \times \frac{\frac{m^2} 4}{\frac 2{n^2}}$$
$$\frac{64n}{m^3} \times \frac{m^2n^2}{8}$$
$$\frac{64n \times m^2n^2}{8m^3}$$
$$\frac{64m^2n^3}{8m^3}$$
$$\frac{8n^3} m=8m^{-1}n^3$$

## Discussion (2)

• You should solve it according to how you wrote it,please

• $$\left[\frac{\sqrt[8]n}{m^{\frac 3 2}}\right]^2\left[\frac{4^{-1}m^2}{2n^{-2}}\right]=(8\sqrt n)^2$$
$$\frac{64n}{m^3} \times \frac{\frac 1 4 \times m^2}{2 \times \frac 1{n^2}}$$
$$\frac{64n}{m^3} \times \frac{\frac{m^2} 4}{\frac 2{n^2}}$$
$$\frac{64n}{m^3} \times \frac{m^2n^2}{8}$$
$$\frac{64n \times m^2n^2}{8m^3}$$
$$\frac{64m^2n^3}{8m^3}$$
$$\frac{8n^3} m=8m^{-1}n^3$$