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

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

Evaluate

$$\frac{4\left(ab\right)^{4}}{x^{6}}$$

Solution Steps

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

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

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

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

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

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

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

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

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

$$\frac{2^{2}a^{4}b^{4}}{x^{6}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4a^{4}b^{4}}{x^{6}}$$

Expand

$$\frac{4\left(ab\right)^{4}}{x^{6}}$$

Solution Steps

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

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

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

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

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

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

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

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

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

$$\frac{2^{2}a^{4}b^{4}}{x^{6}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4a^{4}b^{4}}{x^{6}}$$