Solve (-2a/3b)^4

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

Evaluate

$$\frac{16\times \left(\frac{a}{b}\right)^{4}}{81}$$

Solution Steps

Expand \left(-\frac{2a}{3b}\right)^{4}.

$$\left(-1\right)^{4}\times \left(\frac{2a}{3b}\right)^{4}$$

Calculate -1 to the power of 4 and get 1.

$$1\times \left(\frac{2a}{3b}\right)^{4}$$

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

$$1\times \frac{\left(2a\right)^{4}}{\left(3b\right)^{4}}$$

Express 1\times \frac{\left(2a\right)^{4}}{\left(3b\right)^{4}} as a single fraction.

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

Expand \left(2a\right)^{4}.

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

Calculate 2 to the power of 4 and get 16.

$$\frac{16a^{4}}{\left(3b\right)^{4}}$$

Expand \left(3b\right)^{4}.

$$\frac{16a^{4}}{3^{4}b^{4}}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{16a^{4}}{81b^{4}}$$

Expand

$$\frac{16\times \left(\frac{a}{b}\right)^{4}}{81}$$

Solution Steps

Expand \left(-\frac{2a}{3b}\right)^{4}.

$$\left(-1\right)^{4}\times \left(\frac{2a}{3b}\right)^{4}$$

Calculate -1 to the power of 4 and get 1.

$$1\times \left(\frac{2a}{3b}\right)^{4}$$

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

$$1\times \frac{\left(2a\right)^{4}}{\left(3b\right)^{4}}$$

Express 1\times \frac{\left(2a\right)^{4}}{\left(3b\right)^{4}} as a single fraction.

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

Expand \left(2a\right)^{4}.

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

Calculate 2 to the power of 4 and get 16.

$$\frac{16a^{4}}{\left(3b\right)^{4}}$$

Expand \left(3b\right)^{4}.

$$\frac{16a^{4}}{3^{4}b^{4}}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{16a^{4}}{81b^{4}}$$