Answer:
[tex]\frac{7}{4}[/tex] x²
Step-by-step explanation:
Dealing with the numerical part
[tex]\frac{7}{8}[/tex] ÷ [tex]\frac{1}{2}[/tex] = [tex]\frac{7}{8}[/tex] × [tex]\frac{2}{1}[/tex] = [tex]\frac{14}{8}[/tex] = [tex]\frac{7}{4}[/tex]
Using the rule of exponents
[tex]\frac{a^{m} }{a^{n} }[/tex] = [tex]a^{(m-n)}[/tex] , then
[tex]\frac{x^{\frac{1}{2} } }{x^{-\frac{3}{2} } }[/tex]
= [tex]x^{(\frac{1}{2}-(-\frac{3}{2}) }[/tex]
= [tex]x^{(\frac{1}{2}+\frac{3}{2}) }[/tex]
= [tex]x^{\frac{4}{2} }[/tex]
= x²
Then
[tex]\frac{7}{8}[/tex] [tex]x^{\frac{1}{2} }[/tex] ÷ [tex]\frac{1}{2}[/tex] [tex]x^{-\frac{3}{2} }[/tex]
= [tex]\frac{7}{4}[/tex] x²
