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