How do you simplify #(\frac { k ^ (1/2)} { k ^ { 2} } ) ^ { - 3}#?

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Answer 1 · 2017-12-09T01:39:10

#k^(9/2)#

Let's first handle the terms inside the brackets. We can use the rule that #x^a / x^b = x^a-b#

#(k^(1/2)/k^2)^-3#

#(k^(1/2-2))^-3#

#(k^(-3/2))^-3#

#(1/k^(3/2))^-3#

Now let's use the rule that #x^-1=1/x#:

#(k^(3/2)/1)^3=(k^(3/2))^3#

Lastly, let's use the rule #(x^a)^b=x^(ab)#

#k^(3/2xx3)=k^(9/2)#