Solve (2x^2)^2(-3y)^3(-5xz)^3

$$( 2 x ^ { 2 } ) ^ { 2 } ( - 3 y ) ^ { 3 } ( - 5 x z ) ^ { 3 }$$

Evaluate

$$13500x^{7}\left(yz\right)^{3}$$

Solution Steps

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

$$2^{2}\left(x^{2}\right)^{2}\left(-3y\right)^{3}\left(-5xz\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$2^{2}x^{4}\left(-3y\right)^{3}\left(-5xz\right)^{3}$$

Calculate 2 to the power of 2 and get 4.

$$4x^{4}\left(-3y\right)^{3}\left(-5xz\right)^{3}$$

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

$$4x^{4}\left(-3\right)^{3}y^{3}\left(-5xz\right)^{3}$$

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

$$4x^{4}\left(-27\right)y^{3}\left(-5xz\right)^{3}$$

Multiply 4 and -27 to get -108.

$$-108x^{4}y^{3}\left(-5xz\right)^{3}$$

Expand \left(-5xz\right)^{3}.

$$-108x^{4}y^{3}\left(-5\right)^{3}x^{3}z^{3}$$

Calculate -5 to the power of 3 and get -125.

$$-108x^{4}y^{3}\left(-125\right)x^{3}z^{3}$$

Multiply -108 and -125 to get 13500.

$$13500x^{4}y^{3}x^{3}z^{3}$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$13500x^{7}y^{3}z^{3}$$

Expand

$$13500x^{7}\left(yz\right)^{3}$$

Solution Steps

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

$$2^{2}\left(x^{2}\right)^{2}\left(-3y\right)^{3}\left(-5xz\right)^{3}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$2^{2}x^{4}\left(-3y\right)^{3}\left(-5xz\right)^{3}$$

Calculate 2 to the power of 2 and get 4.

$$4x^{4}\left(-3y\right)^{3}\left(-5xz\right)^{3}$$

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

$$4x^{4}\left(-3\right)^{3}y^{3}\left(-5xz\right)^{3}$$

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

$$4x^{4}\left(-27\right)y^{3}\left(-5xz\right)^{3}$$

Multiply 4 and -27 to get -108.

$$-108x^{4}y^{3}\left(-5xz\right)^{3}$$

Expand \left(-5xz\right)^{3}.

$$-108x^{4}y^{3}\left(-5\right)^{3}x^{3}z^{3}$$

Calculate -5 to the power of 3 and get -125.

$$-108x^{4}y^{3}\left(-125\right)x^{3}z^{3}$$

Multiply -108 and -125 to get 13500.

$$13500x^{4}y^{3}x^{3}z^{3}$$

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$13500x^{7}y^{3}z^{3}$$