Solve (-3ab^2c^3)^3div(-2ac)^2

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

Evaluate

$$-\frac{27ab^{6}c^{7}}{4}$$

Solution Steps

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

$$\frac{\left(-3\right)^{3}a^{3}\left(b^{2}\right)^{3}\left(c^{3}\right)^{3}}{\left(-2ac\right)^{2}}$$

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

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

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

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

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

$$\frac{-27a^{3}b^{6}c^{9}}{\left(-2ac\right)^{2}}$$

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

$$\frac{-27a^{3}b^{6}c^{9}}{\left(-2\right)^{2}a^{2}c^{2}}$$

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

$$\frac{-27a^{3}b^{6}c^{9}}{4a^{2}c^{2}}$$

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

$$\frac{-27ab^{6}c^{7}}{4}$$

Expand

$$-\frac{27ab^{6}c^{7}}{4}$$

Solution Steps

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

$$\frac{\left(-3\right)^{3}a^{3}\left(b^{2}\right)^{3}\left(c^{3}\right)^{3}}{\left(-2ac\right)^{2}}$$

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

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

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

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

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

$$\frac{-27a^{3}b^{6}c^{9}}{\left(-2ac\right)^{2}}$$

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

$$\frac{-27a^{3}b^{6}c^{9}}{\left(-2\right)^{2}a^{2}c^{2}}$$

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

$$\frac{-27a^{3}b^{6}c^{9}}{4a^{2}c^{2}}$$

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

$$\frac{-27ab^{6}c^{7}}{4}$$