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

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

### Question

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

### Options

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

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

C) $$8n^4m$$

D) $$8n^3m$$

The correct answer is B.

### Explanation:

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

## Dicussion (1)

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

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