Solve (4x^4yy)^2*2x^3y^4

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

Evaluate

$$32y^{8}x^{11}$$

Solution Steps

Multiply y and y to get y^{2}.

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

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

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

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

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

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

$$4^{2}x^{8}y^{4}\times 2x^{3}y^{4}$$

Calculate 4 to the power of 2 and get 16.

$$16x^{8}y^{4}\times 2x^{3}y^{4}$$

Multiply 16 and 2 to get 32.

$$32x^{8}y^{4}x^{3}y^{4}$$

To multiply powers of the same base, add their exponents. Add 8 and 3 to get 11.

$$32x^{11}y^{4}y^{4}$$

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$32x^{11}y^{8}$$

Expand

$$32y^{8}x^{11}$$

Solution Steps

Multiply y and y to get y^{2}.

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

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

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

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

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

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

$$4^{2}x^{8}y^{4}\times 2x^{3}y^{4}$$

Calculate 4 to the power of 2 and get 16.

$$16x^{8}y^{4}\times 2x^{3}y^{4}$$

Multiply 16 and 2 to get 32.

$$32x^{8}y^{4}x^{3}y^{4}$$

To multiply powers of the same base, add their exponents. Add 8 and 3 to get 11.

$$32x^{11}y^{4}y^{4}$$

To multiply powers of the same base, add their exponents. Add 4 and 4 to get 8.

$$32x^{11}y^{8}$$