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x^{2}y^{2}\left(-x\right)^{2}\left(y^{3}\right)^{2}
Expand \left(\left(-x\right)y^{3}\right)^{2}.
x^{2}y^{2}\left(-x\right)^{2}y^{6}
To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.
x^{2}y^{2}x^{2}y^{6}
Calculate -x to the power of 2 and get x^{2}.
x^{4}y^{2}y^{6}
To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.
x^{4}y^{8}
To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.
x^{2}y^{2}\left(-x\right)^{2}\left(y^{3}\right)^{2}
Expand \left(\left(-x\right)y^{3}\right)^{2}.
x^{2}y^{2}\left(-x\right)^{2}y^{6}
To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.
x^{2}y^{2}x^{2}y^{6}
Calculate -x to the power of 2 and get x^{2}.
x^{4}y^{2}y^{6}
To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.
x^{4}y^{8}
To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.