Solve 2x^2*(-3x^2y^3)^3

$$2 x ^ { 2 } \times ( - 3 x ^ { 2 } y ^ { 3 } ) ^ { 3 }$$

Evaluate

$$-54x^{8}y^{9}$$

Solution Steps

Expand \left(-3x^{2}y^{3}\right)^{3}.

$$2x^{2}\left(-3\right)^{3}\left(x^{2}\right)^{3}\left(y^{3}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$2x^{2}\left(-3\right)^{3}x^{6}\left(y^{3}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$2x^{2}\left(-3\right)^{3}x^{6}y^{9}$$

Calculate -3 to the power of 3 and get -27.

$$2x^{2}\left(-27\right)x^{6}y^{9}$$

Multiply 2 and -27 to get -54.

$$-54x^{2}x^{6}y^{9}$$

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$-54x^{8}y^{9}$$

Expand

$$-54x^{8}y^{9}$$

Solution Steps

Expand \left(-3x^{2}y^{3}\right)^{3}.

$$2x^{2}\left(-3\right)^{3}\left(x^{2}\right)^{3}\left(y^{3}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$2x^{2}\left(-3\right)^{3}x^{6}\left(y^{3}\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$2x^{2}\left(-3\right)^{3}x^{6}y^{9}$$

Calculate -3 to the power of 3 and get -27.

$$2x^{2}\left(-27\right)x^{6}y^{9}$$

Multiply 2 and -27 to get -54.

$$-54x^{2}x^{6}y^{9}$$

To multiply powers of the same base, add their exponents. Add 2 and 6 to get 8.

$$-54x^{8}y^{9}$$