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

$$( - 2 x ^ { 3 } y ^ { i } ) ^ { 3 } \cdot 4 x y ^ { 2 } =$$

Evaluate

$$-32y^{2+3i}x^{10}$$

Solution Steps

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

$$\left(-2\right)^{3}\left(x^{3}\right)^{3}\left(y^{i}\right)^{3}\times 4xy^{2}$$

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

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

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

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

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

$$-8x^{9}y^{3i}\times 4xy^{2}$$

Multiply -8 and 4 to get -32.

$$-32x^{9}y^{3i}xy^{2}$$

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

$$-32x^{10}y^{3i}y^{2}$$

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

$$-32x^{10}y^{2+3i}$$

Expand

$$-32y^{2+3i}x^{10}$$

Solution Steps

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

$$\left(-2\right)^{3}\left(x^{3}\right)^{3}\left(y^{i}\right)^{3}\times 4xy^{2}$$

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

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

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

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

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

$$-8x^{9}y^{3i}\times 4xy^{2}$$

Multiply -8 and 4 to get -32.

$$-32x^{9}y^{3i}xy^{2}$$

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

$$-32x^{10}y^{3i}y^{2}$$

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

$$-32x^{10}y^{2+3i}$$