Solve (2ab^3/-c^2d)^2

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

Evaluate

$$\frac{4\times \left(\frac{a}{d}\right)^{2}b^{6}}{c^{4}}$$

Short Solution Steps

To raise \frac{2ab^{3}}{\left(-c^{2}\right)d} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2ab^{3}\right)^{2}}{\left(\left(-c^{2}\right)d\right)^{2}}$$

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

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

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

$$\frac{2^{2}a^{2}b^{6}}{\left(\left(-c^{2}\right)d\right)^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4a^{2}b^{6}}{\left(\left(-c^{2}\right)d\right)^{2}}$$

Expand \left(\left(-c^{2}\right)d\right)^{2}.

$$\frac{4a^{2}b^{6}}{\left(-c^{2}\right)^{2}d^{2}}$$

Calculate -c^{2} to the power of 2 and get \left(c^{2}\right)^{2}.

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

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

$$\frac{4a^{2}b^{6}}{c^{4}d^{2}}$$

Expand

$$\frac{4\times \left(\frac{a}{d}\right)^{2}b^{6}}{c^{4}}$$

Short Solution Steps

To raise \frac{2ab^{3}}{\left(-c^{2}\right)d} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2ab^{3}\right)^{2}}{\left(\left(-c^{2}\right)d\right)^{2}}$$

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

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

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

$$\frac{2^{2}a^{2}b^{6}}{\left(\left(-c^{2}\right)d\right)^{2}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4a^{2}b^{6}}{\left(\left(-c^{2}\right)d\right)^{2}}$$

Expand \left(\left(-c^{2}\right)d\right)^{2}.

$$\frac{4a^{2}b^{6}}{\left(-c^{2}\right)^{2}d^{2}}$$

Calculate -c^{2} to the power of 2 and get \left(c^{2}\right)^{2}.

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

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

$$\frac{4a^{2}b^{6}}{c^{4}d^{2}}$$