Solve (2a^2)^2/(3a^3)^3

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

Evaluate

$$\frac{4}{27a^{5}}$$

Solution Steps

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

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

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

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

Calculate 2 to the power of 2 and get 4.

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

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

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

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

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

Calculate 3 to the power of 3 and get 27.

$$\frac{4a^{4}}{27a^{9}}$$

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

$$\frac{4}{27a^{5}}$$

Expand

$$\frac{4}{27a^{5}}$$

Solution Steps

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

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

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

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

Calculate 2 to the power of 2 and get 4.

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

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

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

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

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

Calculate 3 to the power of 3 and get 27.

$$\frac{4a^{4}}{27a^{9}}$$

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

$$\frac{4}{27a^{5}}$$