How do you simplify #sqrt(36 a^2 b^-8)#?

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Answer 1 · 2017-01-08T14:54:25

Convert out of radical form and solve using the rules for exponents. See the full explanation below:

First we can rewrite this expression from radical form into exponent form:

#sqrt(36a^2b^-8) = (36a^2b^-8)^(1/2)#

Next we can use this rule for exponents to simplify the parenthesis term:

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

#36^(1/2)a^(2xx1/2)b^(-8xx1/2)#

#6a^1b^(-4)#

We can now use two other rules for exponents to finalize the simplification:

#x^color(red)(1) = x#

#x^color(red)(a) = 1/x^color(red)(-a)#

#(6a)/b^(-(-4))#

#(6a)/b^4#