Solve (-2x^{2}y)^2*xy^3div2x^7y^8

$$( - 2 x ^ { 2 } y ) ^ { 2 } \times x y ^ { 3 } \div 2 x ^ { 7 } y ^ { 8 }$$

Evaluate

$$2x^{12}y^{13}$$

Solution Steps

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

$$\frac{\left(-2\right)^{2}\left(x^{2}\right)^{2}y^{2}xy^{3}}{2}x^{7}y^{8}$$

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

$$\frac{\left(-2\right)^{2}x^{4}y^{2}xy^{3}}{2}x^{7}y^{8}$$

Calculate -2 to the power of 2 and get 4.

$$\frac{4x^{4}y^{2}xy^{3}}{2}x^{7}y^{8}$$

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

$$\frac{4x^{5}y^{2}y^{3}}{2}x^{7}y^{8}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{4x^{5}y^{5}}{2}x^{7}y^{8}$$

Divide 4x^{5}y^{5} by 2 to get 2x^{5}y^{5}.

$$2x^{5}y^{5}x^{7}y^{8}$$

To multiply powers of the same base, add their exponents. Add 5 and 7 to get 12.

$$2x^{12}y^{5}y^{8}$$

To multiply powers of the same base, add their exponents. Add 5 and 8 to get 13.

$$2x^{12}y^{13}$$

Expand

$$2x^{12}y^{13}$$

Solution Steps

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

$$\frac{\left(-2\right)^{2}\left(x^{2}\right)^{2}y^{2}xy^{3}}{2}x^{7}y^{8}$$

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

$$\frac{\left(-2\right)^{2}x^{4}y^{2}xy^{3}}{2}x^{7}y^{8}$$

Calculate -2 to the power of 2 and get 4.

$$\frac{4x^{4}y^{2}xy^{3}}{2}x^{7}y^{8}$$

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

$$\frac{4x^{5}y^{2}y^{3}}{2}x^{7}y^{8}$$

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$\frac{4x^{5}y^{5}}{2}x^{7}y^{8}$$

Divide 4x^{5}y^{5} by 2 to get 2x^{5}y^{5}.

$$2x^{5}y^{5}x^{7}y^{8}$$

To multiply powers of the same base, add their exponents. Add 5 and 7 to get 12.

$$2x^{12}y^{5}y^{8}$$

To multiply powers of the same base, add their exponents. Add 5 and 8 to get 13.

$$2x^{12}y^{13}$$