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Simplify f\(^{\frac{1}{2}}\)g\(^2\)h\(^{\frac{1}{3}}\) \(\div\) f\(^{\frac{5}{2}}\)g\(^o\)h\(^{\frac{7}{3}}\)

Mathematics
JAMB 1982

Simplify f\(^{\frac{1}{2}}\)g\(^2\)h\(^{\frac{1}{3}}\) \(\div\) f\(^{\frac{5}{2}}\)g\(^o\)h\(^{\frac{7}{3}}\)

  • A. (\(\frac{g}{fh}\))2
  • B. f2g2h2
  • C. \(\frac{5}{4}\)goh\(\frac{7}{9}\)
  • D. \(\frac{g^2}{f^5h^7}\)
  • E. \(\frac{1}{f^2h^2}\)
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Correct Answer: Option A
Explanation

f\(^{\frac{1}{2}}\)g\(^2\)h\(^{\frac{1}{3}}\) \(\div\) f\(^{\frac{5}{2}}\)g\(^o\)h\(^{\frac{7}{3}}\) = f\(^{\frac{1}{2} - \frac{5}{2}}\) g\(^{2 - 0}\) h\(^{\frac{1}{3} - \frac{7}{3}}\)

= f\(^{-2}\) g\(^2\) h\(^{-2}\)

= \(\frac{g^2}{f^2h^2}\)

= (\(\frac{g}{fh}\))\(^2\)


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