Rewrite expressions with radicals and rational exponents using exponent properties.
Simplify radicals with variable exponents by pulling out perfect powers
Problem
Simplify \(\sqrt{x^{7}}\) by writing \(x^{7}=x^{6}\cdot~x\) and taking the square root of the greatest even power.
Big Picture
What this problem is really about
Variable powers leave the radical in complete pairs determined by the root index. We’ll separate the greatest even exponent, establish the real domain, take the principal root of the paired power without an absolute-value mismatch on that domain, and leave the unpaired factor inside.
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