SOLUTION: Simplify? the square root of 16z to the 12 power

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Question 102471: Simplify? the square root of 16z to the 12 power
Found 2 solutions by jim_thompson5910, Fombitz:
Answer by jim_thompson5910(21667) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%2816%2Az%5E12%29Start with the given expression
sqrt%2816%2Az%5E2%2Az%5E2%2Az%5E2%2Az%5E2%2Az%5E2%2Az%5E2%29 Factor z%5E12 into z%5E2%2Az%5E2%2Az%5E2%2Az%5E2%2Az%5E2%2Az%5E2

sqrt%2816%29%2Asqrt%28z%5E2%29%2Asqrt%28z%5E2%29%2Asqrt%28z%5E2%29%2Asqrt%28z%5E2%29%2Asqrt%28z%5E2%29%2Asqrt%28z%5E2%29 Break up the square root using the identity sqrt%28x%2Ay%29=sqrt%28x%29%2Asqrt%28y%29

4%2Asqrt%28z%5E2%29%2Asqrt%28z%5E2%29%2Asqrt%28z%5E2%29%2Asqrt%28z%5E2%29%2Asqrt%28z%5E2%29%2Asqrt%28z%5E2%29 Take the square root of the perfect square 16 to get 4

4%2Az%2Az%2Az%2Az%2Az%2Az Take the square root of the perfect squares z%5E2 to get z

4%2Az%5E6 Multiply the common terms

Answer by Fombitz(13823) About Me  (Show Source):
You can put this solution on YOUR website!
Is this what you mean?
sqrt%2816z%5E12%29=%2816z%5E12%29%5E%281%2F2%29 The square root means raised to the power of 1/2.
When you have an exponent expression raised to a power, you multiply the exponents, such as
%28x%5Em%2Ay%5Ep%29%5En+=+x%5E%28m%2An%29%2Ay%5E%28p%2An%29
Back to your problem
sqrt%2816z%5E12%29=%2816z%5E12%29%5E%281%2F2%29
sqrt%2816z%5E12%29=16%5E%281%2F2%29%2Az%5E%2812%2A%281%2F2%29%29
sqrt%2816z%5E12%29=4z%5E%286%29