Solve (2yx^4)^2*(2y^3)^2

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

Evaluate

$$16\left(xy\right)^{8}$$

Solution Steps

Expand \left(2yx^{4}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$2^{2}y^{2}x^{8}\times \left(2y^{3}\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$4y^{2}x^{8}\times \left(2y^{3}\right)^{2}$$

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

$$4y^{2}x^{8}\times 2^{2}\left(y^{3}\right)^{2}$$

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

$$4y^{2}x^{8}\times 2^{2}y^{6}$$

Calculate 2 to the power of 2 and get 4.

$$4y^{2}x^{8}\times 4y^{6}$$

Multiply 4 and 4 to get 16.

$$16y^{2}x^{8}y^{6}$$

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

$$16y^{8}x^{8}$$

Expand

$$16\left(xy\right)^{8}$$

Solution Steps

Expand \left(2yx^{4}\right)^{2}.

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

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$2^{2}y^{2}x^{8}\times \left(2y^{3}\right)^{2}$$

Calculate 2 to the power of 2 and get 4.

$$4y^{2}x^{8}\times \left(2y^{3}\right)^{2}$$

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

$$4y^{2}x^{8}\times 2^{2}\left(y^{3}\right)^{2}$$

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

$$4y^{2}x^{8}\times 2^{2}y^{6}$$

Calculate 2 to the power of 2 and get 4.

$$4y^{2}x^{8}\times 4y^{6}$$

Multiply 4 and 4 to get 16.

$$16y^{2}x^{8}y^{6}$$

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

$$16y^{8}x^{8}$$