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
\(\frac{1}{f^2h^2}\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
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\(^{-2}\)
= \(\frac{g^2}{f^2h^2}\)
= (\(\frac{g}{fh}\))\(^2\)
Source: Myschool Past Questions Archive (Record #32539)