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3 years ago

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

Mathematics

1 answer:

Vlad1618 [11]3 years ago

7 0

Answer:

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

Step-by-step explanation:

<u><em>Explanation</em></u>

Given

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

By using algebra formulas

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

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

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

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

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

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

<u><em>Final answer:-</em></u>

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

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