Answer:
[tex]\frac{1}{5}[/tex]
Step-by-step explanation:
Using the properties of exponents / radicals
• [tex](a^m)^{n}[/tex] = [tex]a^{mn}[/tex]
• [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]
• [tex]a^{\frac{1}{2} }[/tex] = [tex]\sqrt{a}[/tex]
given
[tex](25^{-\frac{3}{2}) } ^{\frac{1}{3} }[/tex]
= [tex]25^{-\frac{3}{2} } ^{(\frac{1}{3}) }[/tex]
= [tex]25^{-\frac{1}{2} }[/tex]
= [tex]\frac{1}{25^{\frac{1}{2} } }[/tex]
= [tex]\frac{1}{\sqrt{25} }[/tex]
= [tex]\frac{1}{5}[/tex]