Solve bc/(3a^3b^2c^2)^3

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

Evaluate

$$\frac{1}{27a^{9}\left(bc\right)^{5}}$$

Solution Steps

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

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

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

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

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

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

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

$$\frac{bc}{3^{3}a^{9}b^{6}c^{6}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{bc}{27a^{9}b^{6}c^{6}}$$

Cancel out bc in both numerator and denominator.

$$\frac{1}{27b^{5}c^{5}a^{9}}$$

Expand

$$\frac{1}{27a^{9}\left(bc\right)^{5}}$$

Solution Steps

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

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

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

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

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

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

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

$$\frac{bc}{3^{3}a^{9}b^{6}c^{6}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{bc}{27a^{9}b^{6}c^{6}}$$

Cancel out bc in both numerator and denominator.

$$\frac{1}{27b^{5}c^{5}a^{9}}$$