Question

Simplify (8^4/10^4)^-1/4using rational exponents

Answer 1

Answer:

   $(\frac{8^4}{10^4} )^{-\frac{1}{4} }$  = $\frac{5}{4}$

Step-by-step explanation:

Explanation

Given  

       $(\frac{8^4}{10^4} )^{-\frac{1}{4} }$

By using algebra formulas

  $(\frac{a}{b} )^{m} = \frac{a^m}{b^n}$

$(\frac{8^4}{10^4} )^{-\frac{1}{4} } = \frac{(8^{4})^{\frac{-1}{4} } }{(10^{4} )^{\frac{-1}{4} } }$

$(a^{m} )^{n} = a^{mn}$

$\frac{(8^{4})^{\frac{-1}{4} } }{(10^{4} )^{\frac{-1}{4} } } = \frac{8^{4X\frac{-1}{4} } }{10^{4 X\frac{-1}{4} } }$

          = $\frac{8^{-1} }{10^{-1} }$

           $= \frac{10}{8} \\= \frac{5}{4}$

Final answer:-

 $(\frac{8^4}{10^4} )^{-\frac{1}{4} }$  = $\frac{5}{4}$