Solve 11(2a/5n)^3

$$11 ( \frac { 2 a } { 5 n } ) ^ { 3 }$$

Evaluate

$$\frac{88\times \left(\frac{a}{n}\right)^{3}}{125}$$

Solution Steps

To raise \frac{2a}{5n} to a power, raise both numerator and denominator to the power and then divide.

$$11\times \frac{\left(2a\right)^{3}}{\left(5n\right)^{3}}$$

Express 11\times \frac{\left(2a\right)^{3}}{\left(5n\right)^{3}} as a single fraction.

$$\frac{11\times \left(2a\right)^{3}}{\left(5n\right)^{3}}$$

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

$$\frac{11\times 2^{3}a^{3}}{\left(5n\right)^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{11\times 8a^{3}}{\left(5n\right)^{3}}$$

Multiply 11 and 8 to get 88.

$$\frac{88a^{3}}{\left(5n\right)^{3}}$$

Expand \left(5n\right)^{3}.

$$\frac{88a^{3}}{5^{3}n^{3}}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{88a^{3}}{125n^{3}}$$

Expand

$$\frac{88\times \left(\frac{a}{n}\right)^{3}}{125}$$

Solution Steps

To raise \frac{2a}{5n} to a power, raise both numerator and denominator to the power and then divide.

$$11\times \frac{\left(2a\right)^{3}}{\left(5n\right)^{3}}$$

Express 11\times \frac{\left(2a\right)^{3}}{\left(5n\right)^{3}} as a single fraction.

$$\frac{11\times \left(2a\right)^{3}}{\left(5n\right)^{3}}$$

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

$$\frac{11\times 2^{3}a^{3}}{\left(5n\right)^{3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{11\times 8a^{3}}{\left(5n\right)^{3}}$$

Multiply 11 and 8 to get 88.

$$\frac{88a^{3}}{\left(5n\right)^{3}}$$

Expand \left(5n\right)^{3}.

$$\frac{88a^{3}}{5^{3}n^{3}}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{88a^{3}}{125n^{3}}$$