How do you simplify #12^(10/8)/12^(-3/8)#?

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Answer 1 · 2017-06-08T01:57:27

See a solution process below:

Use the following rule for exponents to simplify: #x^color(red)(a)/x^color(blue)(b) = x^(color(red)(a)-color(blue)(b))#

#12^color(red)(10/8)/12^color(blue)(-3/8) = 12^(color(red)(10/8)-color(blue)(-3/8)) = 12^(color(red)(10/8)+color(blue)(3/8)) = 12^(13/8)#

We can also rewrite this expression as:

#12^(13 xx 1/8)#

We can now use this rule of exponents to rewrite the expression again as:

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

#12^(color(red)(13) xx color(blue)(1/8)) = (12^color(red)(13))^color(blue)(1/8)#

If we want to simplify this to write the expression in radical form we can use this rule of exponents:

#(12^13)^(1/color(red)(8)) = root(color(red)(8))(12^13)#