Solve frac{(3ab^{2})^3}{(2a^3b^2)^2}

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

Evaluate

$$\frac{27b^{2}}{4a^{3}}$$

Solution Steps

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

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

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

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

Calculate 3 to the power of 3 and get 27.

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

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

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

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

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

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

$$\frac{27a^{3}b^{6}}{2^{2}a^{6}b^{4}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{27a^{3}b^{6}}{4a^{6}b^{4}}$$

Cancel out a^{3}b^{4} in both numerator and denominator.

$$\frac{27b^{2}}{4a^{3}}$$

Expand

$$\frac{27b^{2}}{4a^{3}}$$

Solution Steps

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

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

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

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

Calculate 3 to the power of 3 and get 27.

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

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

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

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

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

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

$$\frac{27a^{3}b^{6}}{2^{2}a^{6}b^{4}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{27a^{3}b^{6}}{4a^{6}b^{4}}$$

Cancel out a^{3}b^{4} in both numerator and denominator.

$$\frac{27b^{2}}{4a^{3}}$$