Solve (-3a^{3}b^{2}c)^{3}*2ac^{3}div(-18a^{4}b^5)div(3a^2c^2)^3

$$( - 3 a ^ { 3 } b ^ { 2 } c ) ^ { 3 } \cdot 2 a c ^ { 3 } \div ( - 18 a ^ { 4 } b ^ { 5 } ) \div ( 3 a ^ { 2 } c ^ { 2 } ) ^ { 3 }$$

Evaluate

$$\frac{b}{9}$$

Solution Steps

Cancel out 2a in both numerator and denominator.

$$\frac{\frac{c^{3}\left(-3cb^{2}a^{3}\right)^{3}}{-9a^{3}b^{5}}}{\left(3a^{2}c^{2}\right)^{3}}$$

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

$$\frac{\frac{c^{3}\left(-3\right)^{3}c^{3}\left(b^{2}\right)^{3}\left(a^{3}\right)^{3}}{-9a^{3}b^{5}}}{\left(3a^{2}c^{2}\right)^{3}}$$

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

$$\frac{\frac{c^{3}\left(-3\right)^{3}c^{3}b^{6}\left(a^{3}\right)^{3}}{-9a^{3}b^{5}}}{\left(3a^{2}c^{2}\right)^{3}}$$

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

$$\frac{\frac{c^{3}\left(-3\right)^{3}c^{3}b^{6}a^{9}}{-9a^{3}b^{5}}}{\left(3a^{2}c^{2}\right)^{3}}$$

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

$$\frac{\frac{c^{3}\left(-27\right)c^{3}b^{6}a^{9}}{-9a^{3}b^{5}}}{\left(3a^{2}c^{2}\right)^{3}}$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$\frac{\frac{c^{6}\left(-27\right)b^{6}a^{9}}{-9a^{3}b^{5}}}{\left(3a^{2}c^{2}\right)^{3}}$$

Cancel out 9a^{3}b^{5} in both numerator and denominator.

$$\frac{\frac{-3ba^{6}c^{6}}{-1}}{\left(3a^{2}c^{2}\right)^{3}}$$

Anything divided by -1 gives its opposite.

$$\frac{3ba^{6}c^{6}}{\left(3a^{2}c^{2}\right)^{3}}$$

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

$$\frac{3ba^{6}c^{6}}{3^{3}\left(a^{2}\right)^{3}\left(c^{2}\right)^{3}}$$

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

$$\frac{3ba^{6}c^{6}}{3^{3}a^{6}\left(c^{2}\right)^{3}}$$

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

$$\frac{3ba^{6}c^{6}}{3^{3}a^{6}c^{6}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{3ba^{6}c^{6}}{27a^{6}c^{6}}$$

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

$$\frac{b}{9}$$

Expand

$$\frac{b}{9}$$

Solution Steps

Cancel out 2a in both numerator and denominator.

$$\frac{\frac{c^{3}\left(-3cb^{2}a^{3}\right)^{3}}{-9a^{3}b^{5}}}{\left(3a^{2}c^{2}\right)^{3}}$$

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

$$\frac{\frac{c^{3}\left(-3\right)^{3}c^{3}\left(b^{2}\right)^{3}\left(a^{3}\right)^{3}}{-9a^{3}b^{5}}}{\left(3a^{2}c^{2}\right)^{3}}$$

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

$$\frac{\frac{c^{3}\left(-3\right)^{3}c^{3}b^{6}\left(a^{3}\right)^{3}}{-9a^{3}b^{5}}}{\left(3a^{2}c^{2}\right)^{3}}$$

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

$$\frac{\frac{c^{3}\left(-3\right)^{3}c^{3}b^{6}a^{9}}{-9a^{3}b^{5}}}{\left(3a^{2}c^{2}\right)^{3}}$$

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

$$\frac{\frac{c^{3}\left(-27\right)c^{3}b^{6}a^{9}}{-9a^{3}b^{5}}}{\left(3a^{2}c^{2}\right)^{3}}$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$\frac{\frac{c^{6}\left(-27\right)b^{6}a^{9}}{-9a^{3}b^{5}}}{\left(3a^{2}c^{2}\right)^{3}}$$

Cancel out 9a^{3}b^{5} in both numerator and denominator.

$$\frac{\frac{-3ba^{6}c^{6}}{-1}}{\left(3a^{2}c^{2}\right)^{3}}$$

Anything divided by -1 gives its opposite.

$$\frac{3ba^{6}c^{6}}{\left(3a^{2}c^{2}\right)^{3}}$$

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

$$\frac{3ba^{6}c^{6}}{3^{3}\left(a^{2}\right)^{3}\left(c^{2}\right)^{3}}$$

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

$$\frac{3ba^{6}c^{6}}{3^{3}a^{6}\left(c^{2}\right)^{3}}$$

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

$$\frac{3ba^{6}c^{6}}{3^{3}a^{6}c^{6}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{3ba^{6}c^{6}}{27a^{6}c^{6}}$$

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

$$\frac{b}{9}$$