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\left(-7x^{2}\right)^{1}\times \frac{1}{-7x^{2}}
Use the rules of exponents to simplify the expression.
\left(-7\right)^{1}\left(x^{2}\right)^{1}\times \frac{1}{-7}\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(-7\right)^{1}\times \frac{1}{-7}\left(x^{2}\right)^{1}\times \frac{1}{x^{2}}
Use the Commutative Property of Multiplication.
\left(-7\right)^{1}\times \frac{1}{-7}x^{2}x^{2\left(-1\right)}
To raise a power to another power, multiply the exponents.
\left(-7\right)^{1}\times \frac{1}{-7}x^{2}x^{-2}
Multiply 2 times -1.
\left(-7\right)^{1}\times \frac{1}{-7}x^{2-2}
To multiply powers of the same base, add their exponents.
\left(-7\right)^{1}\times \frac{1}{-7}x^{0}
Add the exponents 2 and -2.
\left(-7\right)^{1-1}x^{0}
To multiply powers of the same base, add their exponents.
\left(-7\right)^{0}x^{0}
Add the exponents 1 and -1.
1\times 1
For any term t except 0, t^{0}=1.
1
For any term t, t\times 1=t and 1t=t.
\frac{\left(-7\right)^{1}x^{2}}{\left(-7\right)^{1}x^{2}}
Use the rules of exponents to simplify the expression.
\left(-7\right)^{1-1}x^{2-2}
To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.
\left(-7\right)^{0}x^{2-2}
Subtract 1 from 1.
x^{2-2}
For any number a except 0, a^{0}=1.
x^{0}
Subtract 2 from 2.
1
For any number a except 0, a^{0}=1.