Solve (3a^3bc)^3/27bc^4*9a/8bdiv3b/4a^4c

$$\frac { ( 3 a ^ { 3 } b c ) ^ { 3 } } { 27 b c ^ { 4 } } \times \frac { 9 a } { 8 b } \div \frac { 3 b } { 4 a ^ { 4 } c }$$

Evaluate

$$\frac{3a^{14}}{2}$$

Solution Steps

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

$$\frac{\frac{3^{3}\left(a^{3}\right)^{3}b^{3}c^{3}}{27bc^{4}}\times \frac{9a}{8b}}{\frac{3b}{4a^{4}c}}$$

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

$$\frac{\frac{3^{3}a^{9}b^{3}c^{3}}{27bc^{4}}\times \frac{9a}{8b}}{\frac{3b}{4a^{4}c}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{\frac{27a^{9}b^{3}c^{3}}{27bc^{4}}\times \frac{9a}{8b}}{\frac{3b}{4a^{4}c}}$$

Cancel out 27bc^{3} in both numerator and denominator.

$$\frac{\frac{b^{2}a^{9}}{c}\times \frac{9a}{8b}}{\frac{3b}{4a^{4}c}}$$

Multiply \frac{b^{2}a^{9}}{c} times \frac{9a}{8b} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{b^{2}a^{9}\times 9a}{c\times 8b}}{\frac{3b}{4a^{4}c}}$$

Cancel out b in both numerator and denominator.

$$\frac{\frac{9aba^{9}}{8c}}{\frac{3b}{4a^{4}c}}$$

Divide \frac{9aba^{9}}{8c} by \frac{3b}{4a^{4}c} by multiplying \frac{9aba^{9}}{8c} by the reciprocal of \frac{3b}{4a^{4}c}.

$$\frac{9aba^{9}\times 4a^{4}c}{8c\times 3b}$$

Cancel out 3\times 4bc in both numerator and denominator.

$$\frac{3aa^{4}a^{9}}{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$\frac{3a^{5}a^{9}}{2}$$

To multiply powers of the same base, add their exponents. Add 5 and 9 to get 14.

$$\frac{3a^{14}}{2}$$

Expand

$$\frac{3a^{14}}{2}$$

Solution Steps

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

$$\frac{\frac{3^{3}\left(a^{3}\right)^{3}b^{3}c^{3}}{27bc^{4}}\times \frac{9a}{8b}}{\frac{3b}{4a^{4}c}}$$

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

$$\frac{\frac{3^{3}a^{9}b^{3}c^{3}}{27bc^{4}}\times \frac{9a}{8b}}{\frac{3b}{4a^{4}c}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{\frac{27a^{9}b^{3}c^{3}}{27bc^{4}}\times \frac{9a}{8b}}{\frac{3b}{4a^{4}c}}$$

Cancel out 27bc^{3} in both numerator and denominator.

$$\frac{\frac{b^{2}a^{9}}{c}\times \frac{9a}{8b}}{\frac{3b}{4a^{4}c}}$$

Multiply \frac{b^{2}a^{9}}{c} times \frac{9a}{8b} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{b^{2}a^{9}\times 9a}{c\times 8b}}{\frac{3b}{4a^{4}c}}$$

Cancel out b in both numerator and denominator.

$$\frac{\frac{9aba^{9}}{8c}}{\frac{3b}{4a^{4}c}}$$

Divide \frac{9aba^{9}}{8c} by \frac{3b}{4a^{4}c} by multiplying \frac{9aba^{9}}{8c} by the reciprocal of \frac{3b}{4a^{4}c}.

$$\frac{9aba^{9}\times 4a^{4}c}{8c\times 3b}$$

Cancel out 3\times 4bc in both numerator and denominator.

$$\frac{3aa^{4}a^{9}}{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$\frac{3a^{5}a^{9}}{2}$$

To multiply powers of the same base, add their exponents. Add 5 and 9 to get 14.

$$\frac{3a^{14}}{2}$$