Solve (-3a^{2}b)^{3}*(-2ab^4)^2div(6a^5b^3)

$$( - 3 a ^ { 2 } b ) ^ { 3 } \cdot ( - 2 a b ^ { 4 } ) ^ { 2 } \div ( 6 a ^ { 5 } b ^ { 3 } )$$

Evaluate

$$-18a^{3}b^{8}$$

Solution Steps

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

$$\frac{\left(-3\right)^{3}\left(a^{2}\right)^{3}b^{3}\left(-2ab^{4}\right)^{2}}{6a^{5}b^{3}}$$

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

$$\frac{\left(-3\right)^{3}a^{6}b^{3}\left(-2ab^{4}\right)^{2}}{6a^{5}b^{3}}$$

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

$$\frac{-27a^{6}b^{3}\left(-2ab^{4}\right)^{2}}{6a^{5}b^{3}}$$

Expand \left(-2ab^{4}\right)^{2}.

$$\frac{-27a^{6}b^{3}\left(-2\right)^{2}a^{2}\left(b^{4}\right)^{2}}{6a^{5}b^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{-27a^{6}b^{3}\left(-2\right)^{2}a^{2}b^{8}}{6a^{5}b^{3}}$$

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

$$\frac{-27a^{6}b^{3}\times 4a^{2}b^{8}}{6a^{5}b^{3}}$$

Multiply -27 and 4 to get -108.

$$\frac{-108a^{6}b^{3}a^{2}b^{8}}{6a^{5}b^{3}}$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$\frac{-108a^{8}b^{3}b^{8}}{6a^{5}b^{3}}$$

To multiply powers of the same base, add their exponents. Add 3 and 8 to get 11.

$$\frac{-108a^{8}b^{11}}{6a^{5}b^{3}}$$

Cancel out 6b^{3}a^{5} in both numerator and denominator.

$$-18a^{3}b^{8}$$

Expand

$$-18a^{3}b^{8}$$

Solution Steps

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

$$\frac{\left(-3\right)^{3}\left(a^{2}\right)^{3}b^{3}\left(-2ab^{4}\right)^{2}}{6a^{5}b^{3}}$$

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

$$\frac{\left(-3\right)^{3}a^{6}b^{3}\left(-2ab^{4}\right)^{2}}{6a^{5}b^{3}}$$

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

$$\frac{-27a^{6}b^{3}\left(-2ab^{4}\right)^{2}}{6a^{5}b^{3}}$$

Expand \left(-2ab^{4}\right)^{2}.

$$\frac{-27a^{6}b^{3}\left(-2\right)^{2}a^{2}\left(b^{4}\right)^{2}}{6a^{5}b^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 2 to get 8.

$$\frac{-27a^{6}b^{3}\left(-2\right)^{2}a^{2}b^{8}}{6a^{5}b^{3}}$$

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

$$\frac{-27a^{6}b^{3}\times 4a^{2}b^{8}}{6a^{5}b^{3}}$$

Multiply -27 and 4 to get -108.

$$\frac{-108a^{6}b^{3}a^{2}b^{8}}{6a^{5}b^{3}}$$

To multiply powers of the same base, add their exponents. Add 6 and 2 to get 8.

$$\frac{-108a^{8}b^{3}b^{8}}{6a^{5}b^{3}}$$

To multiply powers of the same base, add their exponents. Add 3 and 8 to get 11.

$$\frac{-108a^{8}b^{11}}{6a^{5}b^{3}}$$

Cancel out 6b^{3}a^{5} in both numerator and denominator.

$$-18a^{3}b^{8}$$