Answer:
x = ±6^(1/2)
x = ±√6
Step-by-step explanation:
We know that even powers of odd numbers give the same result as even powers of even numbers. That is, x may be positive or negative. We can find the solutions by raising both sides of the equation to the 1/2 power.
(x^2)^(1/2) = 6^(1/2)
x = ±6^(1/2)
x = ±√6
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Additional comment
The rule of exponents that lets us simplify (x^2)^(1/2) is ...
(a^b)^c = a^(bc)
That means (x^2)^(1/2) = x^(2/2) = x^1 = x.
The denominator of a fractional exponent can be written as the index in a radical expression:
[tex]x^{1/n}=\sqrt[n]{x}[/tex]
