Solve (4t^2/5v)^3

$$( \frac { 4 t ^ { 2 } } { 5 v } ) ^ { 3 }$$

Evaluate

$$\frac{64t^{6}}{125v^{3}}$$

Solution Steps

To raise \frac{4t^{2}}{5v} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(4t^{2}\right)^{3}}{\left(5v\right)^{3}}$$

Expand \left(4t^{2}\right)^{3}.

$$\frac{4^{3}\left(t^{2}\right)^{3}}{\left(5v\right)^{3}}$$

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

$$\frac{4^{3}t^{6}}{\left(5v\right)^{3}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{64t^{6}}{\left(5v\right)^{3}}$$

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

$$\frac{64t^{6}}{5^{3}v^{3}}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{64t^{6}}{125v^{3}}$$

Expand

$$\frac{64t^{6}}{125v^{3}}$$

Solution Steps

To raise \frac{4t^{2}}{5v} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(4t^{2}\right)^{3}}{\left(5v\right)^{3}}$$

Expand \left(4t^{2}\right)^{3}.

$$\frac{4^{3}\left(t^{2}\right)^{3}}{\left(5v\right)^{3}}$$

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

$$\frac{4^{3}t^{6}}{\left(5v\right)^{3}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{64t^{6}}{\left(5v\right)^{3}}$$

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

$$\frac{64t^{6}}{5^{3}v^{3}}$$

Calculate 5 to the power of 3 and get 125.

$$\frac{64t^{6}}{125v^{3}}$$