Home » Past Questions » Mathematics » 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:

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

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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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