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

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

Evaluate

$$\frac{9\times \left(\frac{x}{b}\right)^{2}\times \left(\frac{y}{a}\right)^{4}}{4}$$

Solution Steps

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

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

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

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

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

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

Calculate 3 to the power of 2 and get 9.

$$\frac{9x^{2}y^{4}}{\left(2a^{2}b\right)^{2}}$$

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

$$\frac{9x^{2}y^{4}}{2^{2}\left(a^{2}\right)^{2}b^{2}}$$

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

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

Calculate 2 to the power of 2 and get 4.

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

Expand

$$\frac{9\times \left(\frac{x}{b}\right)^{2}\times \left(\frac{y}{a}\right)^{4}}{4}$$

Solution Steps

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

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

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

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

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

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

Calculate 3 to the power of 2 and get 9.

$$\frac{9x^{2}y^{4}}{\left(2a^{2}b\right)^{2}}$$

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

$$\frac{9x^{2}y^{4}}{2^{2}\left(a^{2}\right)^{2}b^{2}}$$

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

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

Calculate 2 to the power of 2 and get 4.

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