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#