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\left(2x^{3}\right)^{1}\times \frac{1}{x^{3}}
Use the rules of exponents to simplify the expression.
2^{1}\left(x^{3}\right)^{1}\times \frac{1}{1}\times \frac{1}{x^{3}}
To raise the product of two or more numbers to a power, raise each number to the power and take their product.
2^{1}\times \frac{1}{1}\left(x^{3}\right)^{1}\times \frac{1}{x^{3}}
Use the Commutative Property of Multiplication.
2^{1}\times \frac{1}{1}x^{3}x^{3\left(-1\right)}
To raise a power to another power, multiply the exponents.
2^{1}\times \frac{1}{1}x^{3}x^{-3}
Multiply 3 times -1.
2^{1}\times \frac{1}{1}x^{3-3}
To multiply powers of the same base, add their exponents.
2^{1}\times \frac{1}{1}x^{0}
Add the exponents 3 and -3.
2\times \frac{1}{1}x^{0}
Raise 2 to the power 1.
2\times \frac{1}{1}\times 1
For any term t except 0, t^{0}=1.
2\times \frac{1}{1}
For any term t, t\times 1=t and 1t=t.