Solve -(2pq^{2})^{3}*(-p^{2}q^3)^2div(p^2q^3)

$$- ( 2 p q ^ { 2 } ) ^ { 3 } \cdot ( - p ^ { 2 } q ^ { 3 } ) ^ { 2 } \div ( p ^ { 2 } q ^ { 3 } )$$

Evaluate

$$-8p^{5}q^{9}$$

Short Solution Steps

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

$$\frac{\left(-2^{3}p^{3}\left(q^{2}\right)^{3}\right)\left(\left(-p^{2}\right)q^{3}\right)^{2}}{p^{2}q^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{\left(-2^{3}p^{3}q^{6}\right)\left(\left(-p^{2}\right)q^{3}\right)^{2}}{p^{2}q^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{\left(-8p^{3}q^{6}\right)\left(\left(-p^{2}\right)q^{3}\right)^{2}}{p^{2}q^{3}}$$

Expand \left(\left(-p^{2}\right)q^{3}\right)^{2}.

$$\frac{\left(-8p^{3}q^{6}\right)\left(-p^{2}\right)^{2}\left(q^{3}\right)^{2}}{p^{2}q^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{\left(-8p^{3}q^{6}\right)\left(-p^{2}\right)^{2}q^{6}}{p^{2}q^{3}}$$

Calculate -p^{2} to the power of 2 and get \left(p^{2}\right)^{2}.

$$\frac{\left(-8p^{3}q^{6}\right)\left(p^{2}\right)^{2}q^{6}}{p^{2}q^{3}}$$

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

$$\frac{q^{3}\left(p^{2}\right)^{2}\left(-8p^{3}q^{6}\right)}{p^{2}}$$

Factor the expressions that are not already factored.

$$\frac{-8p^{3}q^{3}\left(p^{2}\right)^{2}q^{6}}{p^{2}}$$

Cancel out p^{2} in both numerator and denominator.

$$-8pq^{3}\left(p^{2}\right)^{2}q^{6}$$

Expand the expression.

$$-8p^{5}q^{9}$$

Expand

$$-8p^{5}q^{9}$$

Short Solution Steps

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

$$\frac{\left(-2^{3}p^{3}\left(q^{2}\right)^{3}\right)\left(\left(-p^{2}\right)q^{3}\right)^{2}}{p^{2}q^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{\left(-2^{3}p^{3}q^{6}\right)\left(\left(-p^{2}\right)q^{3}\right)^{2}}{p^{2}q^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{\left(-8p^{3}q^{6}\right)\left(\left(-p^{2}\right)q^{3}\right)^{2}}{p^{2}q^{3}}$$

Expand \left(\left(-p^{2}\right)q^{3}\right)^{2}.

$$\frac{\left(-8p^{3}q^{6}\right)\left(-p^{2}\right)^{2}\left(q^{3}\right)^{2}}{p^{2}q^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$\frac{\left(-8p^{3}q^{6}\right)\left(-p^{2}\right)^{2}q^{6}}{p^{2}q^{3}}$$

Calculate -p^{2} to the power of 2 and get \left(p^{2}\right)^{2}.

$$\frac{\left(-8p^{3}q^{6}\right)\left(p^{2}\right)^{2}q^{6}}{p^{2}q^{3}}$$

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

$$\frac{q^{3}\left(p^{2}\right)^{2}\left(-8p^{3}q^{6}\right)}{p^{2}}$$

Factor the expressions that are not already factored.

$$\frac{-8p^{3}q^{3}\left(p^{2}\right)^{2}q^{6}}{p^{2}}$$

Cancel out p^{2} in both numerator and denominator.

$$-8pq^{3}\left(p^{2}\right)^{2}q^{6}$$

Expand the expression.

$$-8p^{5}q^{9}$$