Home » Past Questions » Mathematics » 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) \(8n^4m\)

The correct answer is B.

Explanation:

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

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Discussion (2)

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

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

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