Solve (-5x^2y)*(-4x^3y^2)*(1/2xy)^2

$$( - 5 x ^ { 2 } y ) \cdot ( - 4 x ^ { 3 } y ^ { 2 } ) \cdot ( \frac { 1 } { 2 } x y ) ^ { 2 }$$

Evaluate

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

Solution Steps

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

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

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

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

Multiply -5 and -4 to get 20.

$$20x^{5}y^{3}\times \left(\frac{1}{2}xy\right)^{2}$$

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

$$20x^{5}y^{3}\times \left(\frac{1}{2}\right)^{2}x^{2}y^{2}$$

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

$$20x^{5}y^{3}\times \frac{1}{4}x^{2}y^{2}$$

Multiply 20 and \frac{1}{4} to get 5.

$$5x^{5}y^{3}x^{2}y^{2}$$

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$5x^{7}y^{3}y^{2}$$

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

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

Expand

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

Solution Steps

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

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

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

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

Multiply -5 and -4 to get 20.

$$20x^{5}y^{3}\times \left(\frac{1}{2}xy\right)^{2}$$

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

$$20x^{5}y^{3}\times \left(\frac{1}{2}\right)^{2}x^{2}y^{2}$$

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

$$20x^{5}y^{3}\times \frac{1}{4}x^{2}y^{2}$$

Multiply 20 and \frac{1}{4} to get 5.

$$5x^{5}y^{3}x^{2}y^{2}$$

To multiply powers of the same base, add their exponents. Add 5 and 2 to get 7.

$$5x^{7}y^{3}y^{2}$$

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

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