Answer:
[tex](\frac{8^4}{10^4} )^{-\frac{1}{4} }[/tex] = [tex]\frac{5}{4}[/tex]
Step-by-step explanation:
Explanation
Given
[tex](\frac{8^4}{10^4} )^{-\frac{1}{4} }[/tex]
By using algebra formulas
[tex](\frac{a}{b} )^{m} = \frac{a^m}{b^n}[/tex]
[tex](\frac{8^4}{10^4} )^{-\frac{1}{4} } = \frac{(8^{4})^{\frac{-1}{4} } }{(10^{4} )^{\frac{-1}{4} } }[/tex]
[tex](a^{m} )^{n} = a^{mn}[/tex]
[tex]\frac{(8^{4})^{\frac{-1}{4} } }{(10^{4} )^{\frac{-1}{4} } } = \frac{8^{4X\frac{-1}{4} } }{10^{4 X\frac{-1}{4} } }[/tex]
= [tex]\frac{8^{-1} }{10^{-1} }[/tex]
[tex]= \frac{10}{8} \\= \frac{5}{4}[/tex]
Final answer:-
[tex](\frac{8^4}{10^4} )^{-\frac{1}{4} }[/tex] = [tex]\frac{5}{4}[/tex]
