How do you simplify $(5^2/8^2)^(-1/2)$ ?

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Answer 1 · 2017-02-20T01:08:28

See the entire simplification process below:

Use this rule of exponents to simplify this expression:

$(x^color(red)(a))^color(blue)(b) = x^(color(red)(a) xx color(blue)(b))$

$(5^color(red)(2)/8^color(red)(2))^color(blue)(-1/2) = 5^(color(red)(2)xxcolor(blue)(-1/2))/8^(color(red)(2)xxcolor(blue)(-1/2)) = 5^-1/8^-1$

Next, use these rules for exponents to eliminate the negative exponents:

$x^color(red)(a) = 1/x^color(red)(-a)$ and $1/x^color(red)(a) = x^color(red)(-a)$

$5^color(red)(-1)/8^color(red)(-1) = 8^color(red)(- -1)/5^color(red)(- -1) = 8^1/5^1$

Now, use this rule of exponents to complete the simplification:

$a^color(red)(1) = a$

$8^color(red)(1)/5^color(red)(1) = 8/5$

How do you simplify (5^2/8^2)^(-1/2)(5^2/8^2)^(-1/2)?