Solve (4b^3)^2/(3b^4)^3

$$\frac { ( 4 b ^ { 3 } ) ^ { 2 } } { ( 3 b ^ { 4 } ) ^ { 3 } }$$

Evaluate

$$\frac{16}{27b^{6}}$$

Solution Steps

Expand \left(4b^{3}\right)^{2}.

$$\frac{4^{2}\left(b^{3}\right)^{2}}{\left(3b^{4}\right)^{3}}$$

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

$$\frac{4^{2}b^{6}}{\left(3b^{4}\right)^{3}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{16b^{6}}{\left(3b^{4}\right)^{3}}$$

Expand \left(3b^{4}\right)^{3}.

$$\frac{16b^{6}}{3^{3}\left(b^{4}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{16b^{6}}{3^{3}b^{12}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{16b^{6}}{27b^{12}}$$

Cancel out b^{6} in both numerator and denominator.

$$\frac{16}{27b^{6}}$$

Expand

$$\frac{16}{27b^{6}}$$

Solution Steps

Expand \left(4b^{3}\right)^{2}.

$$\frac{4^{2}\left(b^{3}\right)^{2}}{\left(3b^{4}\right)^{3}}$$

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

$$\frac{4^{2}b^{6}}{\left(3b^{4}\right)^{3}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{16b^{6}}{\left(3b^{4}\right)^{3}}$$

Expand \left(3b^{4}\right)^{3}.

$$\frac{16b^{6}}{3^{3}\left(b^{4}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{16b^{6}}{3^{3}b^{12}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{16b^{6}}{27b^{12}}$$

Cancel out b^{6} in both numerator and denominator.

$$\frac{16}{27b^{6}}$$