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

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

Evaluate

$$-\frac{4}{3a}$$

Solution Steps

Expand \left(-6a^{4}b^{3}\right)^{2}.

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

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

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

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

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

Calculate -6 to the power of 2 and get 36.

$$\frac{36a^{8}b^{6}}{\left(-3a^{3}b^{2}\right)^{3}}$$

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

$$\frac{36a^{8}b^{6}}{\left(-3\right)^{3}\left(a^{3}\right)^{3}\left(b^{2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{36a^{8}b^{6}}{\left(-3\right)^{3}a^{9}\left(b^{2}\right)^{3}}$$

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

$$\frac{36a^{8}b^{6}}{\left(-3\right)^{3}a^{9}b^{6}}$$

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

$$\frac{36a^{8}b^{6}}{-27a^{9}b^{6}}$$

Cancel out 9b^{6}a^{8} in both numerator and denominator.

$$\frac{4}{-3a}$$

Expand

$$-\frac{4}{3a}$$

Solution Steps

Expand \left(-6a^{4}b^{3}\right)^{2}.

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

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

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

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

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

Calculate -6 to the power of 2 and get 36.

$$\frac{36a^{8}b^{6}}{\left(-3a^{3}b^{2}\right)^{3}}$$

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

$$\frac{36a^{8}b^{6}}{\left(-3\right)^{3}\left(a^{3}\right)^{3}\left(b^{2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{36a^{8}b^{6}}{\left(-3\right)^{3}a^{9}\left(b^{2}\right)^{3}}$$

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

$$\frac{36a^{8}b^{6}}{\left(-3\right)^{3}a^{9}b^{6}}$$

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

$$\frac{36a^{8}b^{6}}{-27a^{9}b^{6}}$$

Cancel out 9b^{6}a^{8} in both numerator and denominator.

$$\frac{4}{-3a}$$