Solve 1/2x^{2}y^{3}*(-3xy^{2})+(-2xy)^2*xy^3+(1/4y)^2*(2xy)^3

$$\frac { 1 } { 2 } x ^ { 2 } y ^ { 3 } \times ( - 3 x y ^ { 2 } ) + ( - 2 x y ) ^ { 2 } \cdot x y ^ { 3 } + ( \frac { 1 } { 4 } y ) ^ { 2 } \cdot ( 2 x y ) ^ { 3 }$$

Evaluate

$$3x^{3}y^{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{1}{2}x^{3}y^{3}\left(-3\right)y^{2}+\left(-2xy\right)^{2}xy^{3}+\left(\frac{1}{4}y\right)^{2}\times \left(2xy\right)^{3}$$

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

$$\frac{1}{2}x^{3}y^{5}\left(-3\right)+\left(-2xy\right)^{2}xy^{3}+\left(\frac{1}{4}y\right)^{2}\times \left(2xy\right)^{3}$$

Multiply \frac{1}{2} and -3 to get -\frac{3}{2}.

$$-\frac{3}{2}x^{3}y^{5}+\left(-2xy\right)^{2}xy^{3}+\left(\frac{1}{4}y\right)^{2}\times \left(2xy\right)^{3}$$

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

$$-\frac{3}{2}x^{3}y^{5}+\left(-2\right)^{2}x^{2}y^{2}xy^{3}+\left(\frac{1}{4}y\right)^{2}\times \left(2xy\right)^{3}$$

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

$$-\frac{3}{2}x^{3}y^{5}+4x^{2}y^{2}xy^{3}+\left(\frac{1}{4}y\right)^{2}\times \left(2xy\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$-\frac{3}{2}x^{3}y^{5}+4x^{3}y^{2}y^{3}+\left(\frac{1}{4}y\right)^{2}\times \left(2xy\right)^{3}$$

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

$$-\frac{3}{2}x^{3}y^{5}+4x^{3}y^{5}+\left(\frac{1}{4}y\right)^{2}\times \left(2xy\right)^{3}$$

Combine -\frac{3}{2}x^{3}y^{5} and 4x^{3}y^{5} to get \frac{5}{2}x^{3}y^{5}.

$$\frac{5}{2}x^{3}y^{5}+\left(\frac{1}{4}y\right)^{2}\times \left(2xy\right)^{3}$$

Expand \left(\frac{1}{4}y\right)^{2}.

$$\frac{5}{2}x^{3}y^{5}+\left(\frac{1}{4}\right)^{2}y^{2}\times \left(2xy\right)^{3}$$

Calculate \frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$\frac{5}{2}x^{3}y^{5}+\frac{1}{16}y^{2}\times \left(2xy\right)^{3}$$

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

$$\frac{5}{2}x^{3}y^{5}+\frac{1}{16}y^{2}\times 2^{3}x^{3}y^{3}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{5}{2}x^{3}y^{5}+\frac{1}{16}y^{2}\times 8x^{3}y^{3}$$

Multiply \frac{1}{16} and 8 to get \frac{1}{2}.

$$\frac{5}{2}x^{3}y^{5}+\frac{1}{2}y^{2}x^{3}y^{3}$$

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

$$\frac{5}{2}x^{3}y^{5}+\frac{1}{2}y^{5}x^{3}$$

Combine \frac{5}{2}x^{3}y^{5} and \frac{1}{2}y^{5}x^{3} to get 3x^{3}y^{5}.

$$3x^{3}y^{5}$$

Expand

$$3x^{3}y^{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{1}{2}x^{3}y^{3}\left(-3\right)y^{2}+\left(-2xy\right)^{2}xy^{3}+\left(\frac{1}{4}y\right)^{2}\times \left(2xy\right)^{3}$$

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

$$\frac{1}{2}x^{3}y^{5}\left(-3\right)+\left(-2xy\right)^{2}xy^{3}+\left(\frac{1}{4}y\right)^{2}\times \left(2xy\right)^{3}$$

Multiply \frac{1}{2} and -3 to get -\frac{3}{2}.

$$-\frac{3}{2}x^{3}y^{5}+\left(-2xy\right)^{2}xy^{3}+\left(\frac{1}{4}y\right)^{2}\times \left(2xy\right)^{3}$$

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

$$-\frac{3}{2}x^{3}y^{5}+\left(-2\right)^{2}x^{2}y^{2}xy^{3}+\left(\frac{1}{4}y\right)^{2}\times \left(2xy\right)^{3}$$

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

$$-\frac{3}{2}x^{3}y^{5}+4x^{2}y^{2}xy^{3}+\left(\frac{1}{4}y\right)^{2}\times \left(2xy\right)^{3}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$-\frac{3}{2}x^{3}y^{5}+4x^{3}y^{2}y^{3}+\left(\frac{1}{4}y\right)^{2}\times \left(2xy\right)^{3}$$

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

$$-\frac{3}{2}x^{3}y^{5}+4x^{3}y^{5}+\left(\frac{1}{4}y\right)^{2}\times \left(2xy\right)^{3}$$

Combine -\frac{3}{2}x^{3}y^{5} and 4x^{3}y^{5} to get \frac{5}{2}x^{3}y^{5}.

$$\frac{5}{2}x^{3}y^{5}+\left(\frac{1}{4}y\right)^{2}\times \left(2xy\right)^{3}$$

Expand \left(\frac{1}{4}y\right)^{2}.

$$\frac{5}{2}x^{3}y^{5}+\left(\frac{1}{4}\right)^{2}y^{2}\times \left(2xy\right)^{3}$$

Calculate \frac{1}{4} to the power of 2 and get \frac{1}{16}.

$$\frac{5}{2}x^{3}y^{5}+\frac{1}{16}y^{2}\times \left(2xy\right)^{3}$$

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

$$\frac{5}{2}x^{3}y^{5}+\frac{1}{16}y^{2}\times 2^{3}x^{3}y^{3}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{5}{2}x^{3}y^{5}+\frac{1}{16}y^{2}\times 8x^{3}y^{3}$$

Multiply \frac{1}{16} and 8 to get \frac{1}{2}.

$$\frac{5}{2}x^{3}y^{5}+\frac{1}{2}y^{2}x^{3}y^{3}$$

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

$$\frac{5}{2}x^{3}y^{5}+\frac{1}{2}y^{5}x^{3}$$

Combine \frac{5}{2}x^{3}y^{5} and \frac{1}{2}y^{5}x^{3} to get 3x^{3}y^{5}.

$$3x^{3}y^{5}$$