Suppose (x=a y^{3 / 2}), where (a=7.81 mu mathrm{g} / mathrm{Tm}). Determine the value of (y) when (x=61.7left(mathrm{Eg} cdot mathrm{fm}^{2} ight) /left(mathrm{ms}^{3} ight)). Express the

Suppose \(x=a y^{3 / 2}\), where \(a=7.81 \mu \mathrm{g} / \mathrm{Tm}\). Determine the value of \(y\) when \(x=61.7\left(\mathrm{Eg} \cdot \mathrm{fm}^{2}\right) /\left(\mathrm{ms}^{3}\right)\). Express the result in scientific notation and simplify the units. (Hint: Refer to Principles Table 1.3, and note that SI prefixes are never used to multiply powers of units. For example, the abbreviation \(\mathrm{cm}^{2}\) means \(\left(10^{-2} \mathrm{~m}\right)^{2}\), not \(10^{-2} \mathrm{~m}^{2}\), and \(\mathrm{ns}^{-1}\) is \(1 / \mathrm{ns}\) or \(10^{9} \mathrm{~s}^{-1}\), not \(10^{-9} \mathrm{~s}^{-1}\). Also note that \(\mathrm{m}\) can stand for meter or for milli, depending on the context.)