Solve 9pq^4div(-3q^2)^3*(-6p^2q)

$$9 p q ^ { 4 } \div ( - 3 q ^ { 2 } ) ^ { 3 } \times ( - 6 p ^ { 2 } q )$$

Evaluate

$$\frac{2p^{3}}{q}$$

Solution Steps

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

$$\frac{9pq^{4}}{\left(-3\right)^{3}\left(q^{2}\right)^{3}}\left(-6\right)p^{2}q$$

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

$$\frac{9pq^{4}}{\left(-3\right)^{3}q^{6}}\left(-6\right)p^{2}q$$

Calculate -3 to the power of 3 and get -27.

$$\frac{9pq^{4}}{-27q^{6}}\left(-6\right)p^{2}q$$

Cancel out 9q^{4} in both numerator and denominator.

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

Express \frac{p}{-3q^{2}}\left(-6\right) as a single fraction.

$$\frac{-p\times 6}{-3q^{2}}p^{2}q$$

Cancel out 3 in both numerator and denominator.

$$\frac{-2p}{-q^{2}}p^{2}q$$

Cancel out -1 in both numerator and denominator.

$$\frac{2p}{q^{2}}p^{2}q$$

Express \frac{2p}{q^{2}}p^{2} as a single fraction.

$$\frac{2pp^{2}}{q^{2}}q$$

Express \frac{2pp^{2}}{q^{2}}q as a single fraction.

$$\frac{2pp^{2}q}{q^{2}}$$

Cancel out q in both numerator and denominator.

$$\frac{2pp^{2}}{q}$$

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

$$\frac{2p^{3}}{q}$$

Expand

$$\frac{2p^{3}}{q}$$

Solution Steps

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

$$\frac{9pq^{4}}{\left(-3\right)^{3}\left(q^{2}\right)^{3}}\left(-6\right)p^{2}q$$

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

$$\frac{9pq^{4}}{\left(-3\right)^{3}q^{6}}\left(-6\right)p^{2}q$$

Calculate -3 to the power of 3 and get -27.

$$\frac{9pq^{4}}{-27q^{6}}\left(-6\right)p^{2}q$$

Cancel out 9q^{4} in both numerator and denominator.

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

Express \frac{p}{-3q^{2}}\left(-6\right) as a single fraction.

$$\frac{-p\times 6}{-3q^{2}}p^{2}q$$

Cancel out 3 in both numerator and denominator.

$$\frac{-2p}{-q^{2}}p^{2}q$$

Cancel out -1 in both numerator and denominator.

$$\frac{2p}{q^{2}}p^{2}q$$

Express \frac{2p}{q^{2}}p^{2} as a single fraction.

$$\frac{2pp^{2}}{q^{2}}q$$

Express \frac{2pp^{2}}{q^{2}}q as a single fraction.

$$\frac{2pp^{2}q}{q^{2}}$$

Cancel out q in both numerator and denominator.

$$\frac{2pp^{2}}{q}$$

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

$$\frac{2p^{3}}{q}$$