Solve (-xy)^2*(2x^9y^5)^4

$$( - x y ) ^ { 2 } \cdot ( 2 x ^ { 9 } y ^ { 5 } ) ^ { 4 }$$

Evaluate

$$16y^{22}x^{38}$$

Solution Steps

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

$$\left(-x\right)^{2}y^{2}\times \left(2x^{9}y^{5}\right)^{4}$$

Calculate -x to the power of 2 and get x^{2}.

$$x^{2}y^{2}\times \left(2x^{9}y^{5}\right)^{4}$$

Expand \left(2x^{9}y^{5}\right)^{4}.

$$x^{2}y^{2}\times 2^{4}\left(x^{9}\right)^{4}\left(y^{5}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 9 and 4 to get 36.

$$x^{2}y^{2}\times 2^{4}x^{36}\left(y^{5}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 4 to get 20.

$$x^{2}y^{2}\times 2^{4}x^{36}y^{20}$$

Calculate 2 to the power of 4 and get 16.

$$x^{2}y^{2}\times 16x^{36}y^{20}$$

To multiply powers of the same base, add their exponents. Add 2 and 36 to get 38.

$$x^{38}y^{2}\times 16y^{20}$$

To multiply powers of the same base, add their exponents. Add 2 and 20 to get 22.

$$x^{38}y^{22}\times 16$$

Expand

$$16y^{22}x^{38}$$

Solution Steps

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

$$\left(-x\right)^{2}y^{2}\times \left(2x^{9}y^{5}\right)^{4}$$

Calculate -x to the power of 2 and get x^{2}.

$$x^{2}y^{2}\times \left(2x^{9}y^{5}\right)^{4}$$

Expand \left(2x^{9}y^{5}\right)^{4}.

$$x^{2}y^{2}\times 2^{4}\left(x^{9}\right)^{4}\left(y^{5}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 9 and 4 to get 36.

$$x^{2}y^{2}\times 2^{4}x^{36}\left(y^{5}\right)^{4}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 4 to get 20.

$$x^{2}y^{2}\times 2^{4}x^{36}y^{20}$$

Calculate 2 to the power of 4 and get 16.

$$x^{2}y^{2}\times 16x^{36}y^{20}$$

To multiply powers of the same base, add their exponents. Add 2 and 36 to get 38.

$$x^{38}y^{2}\times 16y^{20}$$

To multiply powers of the same base, add their exponents. Add 2 and 20 to get 22.

$$x^{38}y^{22}\times 16$$