Solve frac{(2abc)^{3}}{(4b^{2}c)^2}*(3ac^2)^5/(9ab)^3

$$\frac { ( 2 a b c ) ^ { 3 } } { ( 4 b ^ { 2 } c ) ^ { 2 } } \times \frac { ( 3 a c ^ { 2 } ) ^ { 5 } } { ( 9 a b ) ^ { 3 } }$$

Evaluate

$$\frac{a^{5}c^{11}}{6b^{4}}$$

Solution Steps

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

$$\frac{2^{3}a^{3}b^{3}c^{3}}{\left(4b^{2}c\right)^{2}}\times \frac{\left(3ac^{2}\right)^{5}}{\left(9ab\right)^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{8a^{3}b^{3}c^{3}}{\left(4b^{2}c\right)^{2}}\times \frac{\left(3ac^{2}\right)^{5}}{\left(9ab\right)^{3}}$$

Expand \left(4b^{2}c\right)^{2}.

$$\frac{8a^{3}b^{3}c^{3}}{4^{2}\left(b^{2}\right)^{2}c^{2}}\times \frac{\left(3ac^{2}\right)^{5}}{\left(9ab\right)^{3}}$$

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

$$\frac{8a^{3}b^{3}c^{3}}{4^{2}b^{4}c^{2}}\times \frac{\left(3ac^{2}\right)^{5}}{\left(9ab\right)^{3}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{8a^{3}b^{3}c^{3}}{16b^{4}c^{2}}\times \frac{\left(3ac^{2}\right)^{5}}{\left(9ab\right)^{3}}$$

Cancel out 8c^{2}b^{3} in both numerator and denominator.

$$\frac{ca^{3}}{2b}\times \frac{\left(3ac^{2}\right)^{5}}{\left(9ab\right)^{3}}$$

Expand \left(3ac^{2}\right)^{5}.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.

$$\frac{ca^{3}}{2b}\times \frac{3^{5}a^{5}c^{10}}{\left(9ab\right)^{3}}$$

Calculate 3 to the power of 5 and get 243.

$$\frac{ca^{3}}{2b}\times \frac{243a^{5}c^{10}}{\left(9ab\right)^{3}}$$

Expand \left(9ab\right)^{3}.

$$\frac{ca^{3}}{2b}\times \frac{243a^{5}c^{10}}{9^{3}a^{3}b^{3}}$$

Calculate 9 to the power of 3 and get 729.

$$\frac{ca^{3}}{2b}\times \frac{243a^{5}c^{10}}{729a^{3}b^{3}}$$

Cancel out 243a^{3} in both numerator and denominator.

$$\frac{ca^{3}}{2b}\times \frac{a^{2}c^{10}}{3b^{3}}$$

Multiply \frac{ca^{3}}{2b} times \frac{a^{2}c^{10}}{3b^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{ca^{3}a^{2}c^{10}}{2b\times 3b^{3}}$$

To multiply powers of the same base, add their exponents. Add 1 and 10 to get 11.

$$\frac{c^{11}a^{3}a^{2}}{2b\times 3b^{3}}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{c^{11}a^{5}}{2b\times 3b^{3}}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{c^{11}a^{5}}{2b^{4}\times 3}$$

Multiply 2 and 3 to get 6.

$$\frac{c^{11}a^{5}}{6b^{4}}$$

Expand

$$\frac{a^{5}c^{11}}{6b^{4}}$$

Solution Steps

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

$$\frac{2^{3}a^{3}b^{3}c^{3}}{\left(4b^{2}c\right)^{2}}\times \frac{\left(3ac^{2}\right)^{5}}{\left(9ab\right)^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{8a^{3}b^{3}c^{3}}{\left(4b^{2}c\right)^{2}}\times \frac{\left(3ac^{2}\right)^{5}}{\left(9ab\right)^{3}}$$

Expand \left(4b^{2}c\right)^{2}.

$$\frac{8a^{3}b^{3}c^{3}}{4^{2}\left(b^{2}\right)^{2}c^{2}}\times \frac{\left(3ac^{2}\right)^{5}}{\left(9ab\right)^{3}}$$

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

$$\frac{8a^{3}b^{3}c^{3}}{4^{2}b^{4}c^{2}}\times \frac{\left(3ac^{2}\right)^{5}}{\left(9ab\right)^{3}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{8a^{3}b^{3}c^{3}}{16b^{4}c^{2}}\times \frac{\left(3ac^{2}\right)^{5}}{\left(9ab\right)^{3}}$$

Cancel out 8c^{2}b^{3} in both numerator and denominator.

$$\frac{ca^{3}}{2b}\times \frac{\left(3ac^{2}\right)^{5}}{\left(9ab\right)^{3}}$$

Expand \left(3ac^{2}\right)^{5}.

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

To raise a power to another power, multiply the exponents. Multiply 2 and 5 to get 10.

$$\frac{ca^{3}}{2b}\times \frac{3^{5}a^{5}c^{10}}{\left(9ab\right)^{3}}$$

Calculate 3 to the power of 5 and get 243.

$$\frac{ca^{3}}{2b}\times \frac{243a^{5}c^{10}}{\left(9ab\right)^{3}}$$

Expand \left(9ab\right)^{3}.

$$\frac{ca^{3}}{2b}\times \frac{243a^{5}c^{10}}{9^{3}a^{3}b^{3}}$$

Calculate 9 to the power of 3 and get 729.

$$\frac{ca^{3}}{2b}\times \frac{243a^{5}c^{10}}{729a^{3}b^{3}}$$

Cancel out 243a^{3} in both numerator and denominator.

$$\frac{ca^{3}}{2b}\times \frac{a^{2}c^{10}}{3b^{3}}$$

Multiply \frac{ca^{3}}{2b} times \frac{a^{2}c^{10}}{3b^{3}} by multiplying numerator times numerator and denominator times denominator.

$$\frac{ca^{3}a^{2}c^{10}}{2b\times 3b^{3}}$$

To multiply powers of the same base, add their exponents. Add 1 and 10 to get 11.

$$\frac{c^{11}a^{3}a^{2}}{2b\times 3b^{3}}$$

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

$$\frac{c^{11}a^{5}}{2b\times 3b^{3}}$$

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{c^{11}a^{5}}{2b^{4}\times 3}$$

Multiply 2 and 3 to get 6.

$$\frac{c^{11}a^{5}}{6b^{4}}$$