Answer:
[tex]\frac{2m^2n^8}{3}[/tex]
Step-by-step explanation:
The given expression is:
[tex](\frac{4m^{-2}n^8}{9m^{-6}n^{-8} })^{\frac{1}{2}}[/tex]
Upon simplifying the above equation, we get
Move [tex]m^{-6}[/tex] to teh numerator and Using the negative exponent rule, we get
=[tex](\frac{4m^{-2}n^8m^6}{9n^{-8} })^{\frac{1}{2}}[/tex]
Move [tex]n^{-8}[/tex] to teh numerator and Using the negative exponent rule, we get
=[tex](\frac{4m^{-2}n^8m^6n^8}{9})^{\frac{1}{2}}[/tex]
=[tex](\frac{4m^{4}n^{16}}{9})^{\frac{1}{2}}[/tex]
=[tex](\frac{(2)^2(m^2)^2(n^8)^2}{(3)^2})^{\frac{1}{2}}[/tex]
=[tex]\frac{2m^2n^8}{3}[/tex]
which is the correct simplified form of the given expression.
