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\left(-5x^{2}\right)^{1}\times \frac{1}{x^{2}}
Use the rules of exponents to simplify the expression.
\left(-5\right)^{1}\left(x^{2}\right)^{1}\times \frac{1}{1}\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(-5\right)^{1}\times \frac{1}{1}\left(x^{2}\right)^{1}\times \frac{1}{x^{2}}
Use the Commutative Property of Multiplication.
\left(-5\right)^{1}\times \frac{1}{1}x^{2}x^{2\left(-1\right)}
To raise a power to another power, multiply the exponents.
\left(-5\right)^{1}\times \frac{1}{1}x^{2}x^{-2}
Multiply 2 times -1.
\left(-5\right)^{1}\times \frac{1}{1}x^{2-2}
To multiply powers of the same base, add their exponents.
\left(-5\right)^{1}\times \frac{1}{1}x^{0}
Add the exponents 2 and -2.
-5\times \frac{1}{1}x^{0}
Raise -5 to the power 1.
-5\times \frac{1}{1}
For any term t except 0, t^{0}=1.