Solve (frac{2a^{5}b^3}{3a^4b^5})^2

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

Evaluate

$$\frac{4a^{2}}{9b^{4}}$$

Solution Steps

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

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

To raise \frac{2a}{3b^{2}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

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

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

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

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

Calculate 3 to the power of 2 and get 9.

$$\frac{4a^{2}}{9b^{4}}$$

Expand

$$\frac{4a^{2}}{9b^{4}}$$

Solution Steps

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

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

To raise \frac{2a}{3b^{2}} to a power, raise both numerator and denominator to the power and then divide.

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

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

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

Calculate 2 to the power of 2 and get 4.

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

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

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

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

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

Calculate 3 to the power of 2 and get 9.

$$\frac{4a^{2}}{9b^{4}}$$