How do you simplify #(sqrt(144x))^6#?

1 Answer
Apr 2, 2018

Answer:

#(sqrt(144x))^6=2985984x^3#

Explanation:

We can rewrite square roots as powers of #1/2#:
#(sqrt(144x))^6=((144x)^(1/2))^6#

Now we can use the following exponent rule:
#(a^n)^m=a^(mn)#

#therefore ((144x)^(1/2))^6=(144x)^(6/2)=(144x)^3#

Now we can use another exponent rule:
#(ab)^n=a^nb^n#

#therefore (144x)^3=144^3*x^3=2985984x^3#