Solve -4x^2y(-2xy^3z)^3=

$$- 4 x ^ { 2 } y ( - 2 x y ^ { 3 } z ) ^ { 3 } =$$

Evaluate

$$32z^{3}x^{5}y^{10}$$

Solution Steps

Expand \left(-2xy^{3}z\right)^{3}.

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

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

$$-4x^{2}y\left(-2\right)^{3}x^{3}y^{9}z^{3}$$

Calculate -2 to the power of 3 and get -8.

$$-4x^{2}y\left(-8\right)x^{3}y^{9}z^{3}$$

Multiply -4 and -8 to get 32.

$$32x^{2}yx^{3}y^{9}z^{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$32x^{5}yy^{9}z^{3}$$

To multiply powers of the same base, add their exponents. Add 1 and 9 to get 10.

$$32x^{5}y^{10}z^{3}$$

Expand

$$32z^{3}x^{5}y^{10}$$

Solution Steps

Expand \left(-2xy^{3}z\right)^{3}.

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

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

$$-4x^{2}y\left(-2\right)^{3}x^{3}y^{9}z^{3}$$

Calculate -2 to the power of 3 and get -8.

$$-4x^{2}y\left(-8\right)x^{3}y^{9}z^{3}$$

Multiply -4 and -8 to get 32.

$$32x^{2}yx^{3}y^{9}z^{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$32x^{5}yy^{9}z^{3}$$

To multiply powers of the same base, add their exponents. Add 1 and 9 to get 10.

$$32x^{5}y^{10}z^{3}$$