Solve (-3x^2y^2)^2*2xy+(xy)^5

$$( - 3 x ^ { 2 } y ^ { 2 } ) ^ { 2 } \cdot 2 x y + ( x y ) ^ { 5 }$$

Evaluate

$$19\left(xy\right)^{5}$$

Solution Steps

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

$$\left(-3\right)^{2}\left(x^{2}\right)^{2}\left(y^{2}\right)^{2}\times 2xy+\left(xy\right)^{5}$$

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

$$\left(-3\right)^{2}x^{4}\left(y^{2}\right)^{2}\times 2xy+\left(xy\right)^{5}$$

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

$$\left(-3\right)^{2}x^{4}y^{4}\times 2xy+\left(xy\right)^{5}$$

Calculate -3 to the power of 2 and get 9.

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

Multiply 9 and 2 to get 18.

$$18x^{4}y^{4}xy+\left(xy\right)^{5}$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$18x^{5}y^{4}y+\left(xy\right)^{5}$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$18x^{5}y^{5}+\left(xy\right)^{5}$$

Expand \left(xy\right)^{5}.

$$18x^{5}y^{5}+x^{5}y^{5}$$

Combine 18x^{5}y^{5} and x^{5}y^{5} to get 19x^{5}y^{5}.

$$19x^{5}y^{5}$$

Expand

$$19\left(xy\right)^{5}$$

Solution Steps

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

$$\left(-3\right)^{2}\left(x^{2}\right)^{2}\left(y^{2}\right)^{2}\times 2xy+\left(xy\right)^{5}$$

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

$$\left(-3\right)^{2}x^{4}\left(y^{2}\right)^{2}\times 2xy+\left(xy\right)^{5}$$

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

$$\left(-3\right)^{2}x^{4}y^{4}\times 2xy+\left(xy\right)^{5}$$

Calculate -3 to the power of 2 and get 9.

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

Multiply 9 and 2 to get 18.

$$18x^{4}y^{4}xy+\left(xy\right)^{5}$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$18x^{5}y^{4}y+\left(xy\right)^{5}$$

To multiply powers of the same base, add their exponents. Add 4 and 1 to get 5.

$$18x^{5}y^{5}+\left(xy\right)^{5}$$

Expand \left(xy\right)^{5}.

$$18x^{5}y^{5}+x^{5}y^{5}$$

Combine 18x^{5}y^{5} and x^{5}y^{5} to get 19x^{5}y^{5}.

$$19x^{5}y^{5}$$