Solve [(-15x^{2}y)*(-1/3xy^{2})*(-2x^2y)]:[(-3x^2y)(-y)^3*(-10/3x^3)]+2=

$$[ ( - 15 x ^ { 2 } y ) \cdot ( - \frac { 1 } { 3 } x y ^ { 2 } ) \cdot ( - 2 x ^ { 2 } y ) ] : [ ( - 3 x ^ { 2 } y ) ( - y ) ^ { 3 } \cdot ( - \frac { 10 } { 3 } x ^ { 3 } ) ] + 2 =$$

Evaluate

$$3$$

Short Solution Steps

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

$$\frac{-15x^{3}y\left(-\frac{1}{3}\right)y^{2}\left(-2\right)x^{2}y}{-3x^{2}y\left(-y\right)^{3}\left(-\frac{10}{3}\right)x^{3}}+2$$

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

$$\frac{-15x^{5}y\left(-\frac{1}{3}\right)y^{2}\left(-2\right)y}{-3x^{2}y\left(-y\right)^{3}\left(-\frac{10}{3}\right)x^{3}}+2$$

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

$$\frac{-15x^{5}y^{3}\left(-\frac{1}{3}\right)\left(-2\right)y}{-3x^{2}y\left(-y\right)^{3}\left(-\frac{10}{3}\right)x^{3}}+2$$

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{-15x^{5}y^{4}\left(-\frac{1}{3}\right)\left(-2\right)}{-3x^{2}y\left(-y\right)^{3}\left(-\frac{10}{3}\right)x^{3}}+2$$

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

$$\frac{-15x^{5}y^{4}\left(-\frac{1}{3}\right)\left(-2\right)}{-3x^{5}y\left(-y\right)^{3}\left(-\frac{10}{3}\right)}+2$$

Cancel out 3yx^{5} in both numerator and denominator.

$$\frac{-5\left(-2\right)\left(-\frac{1}{3}\right)y^{3}}{-\frac{10}{3}\left(-1\right)\left(-y\right)^{3}}+2$$

Multiply -5 and -2 to get 10.

$$\frac{10\left(-\frac{1}{3}\right)y^{3}}{-\frac{10}{3}\left(-1\right)\left(-y\right)^{3}}+2$$

Multiply 10 and -\frac{1}{3} to get -\frac{10}{3}.

$$\frac{-\frac{10}{3}y^{3}}{-\frac{10}{3}\left(-1\right)\left(-y\right)^{3}}+2$$

Multiply -\frac{10}{3} and -1 to get \frac{10}{3}.

$$\frac{-\frac{10}{3}y^{3}}{\frac{10}{3}\left(-y\right)^{3}}+2$$

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

$$\frac{-\frac{10}{3}y^{3}}{\frac{10}{3}\left(-1\right)^{3}y^{3}}+2$$

Calculate -1 to the power of 3 and get -1.

$$\frac{-\frac{10}{3}y^{3}}{\frac{10}{3}\left(-1\right)y^{3}}+2$$

Multiply \frac{10}{3} and -1 to get -\frac{10}{3}.

$$\frac{-\frac{10}{3}y^{3}}{-\frac{10}{3}y^{3}}+2$$

Cancel out y^{3} in both numerator and denominator.

$$\frac{-\frac{10}{3}}{-\frac{10}{3}}+2$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{1}{\left(-\frac{10}{3}\right)^{0}}+2$$

Calculate -\frac{10}{3} to the power of 0 and get 1.

$$\frac{1}{1}+2$$

Anything divided by one gives itself.

$$1+2$$

Add 1 and 2 to get 3.

$$3$$

Factor

$$3$$