Solve (4nt^4/3r^4)^3

$$( \frac { 4 n t ^ { 4 } } { 3 r ^ { 4 } } ) ^ { 3 }$$

Evaluate

$$\frac{64\times \left(\frac{t}{r}\right)^{12}n^{3}}{27}$$

Solution Steps

To raise \frac{4nt^{4}}{3r^{4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(4nt^{4}\right)^{3}}{\left(3r^{4}\right)^{3}}$$

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

$$\frac{4^{3}n^{3}\left(t^{4}\right)^{3}}{\left(3r^{4}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{4^{3}n^{3}t^{12}}{\left(3r^{4}\right)^{3}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{64n^{3}t^{12}}{\left(3r^{4}\right)^{3}}$$

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

$$\frac{64n^{3}t^{12}}{3^{3}\left(r^{4}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{64n^{3}t^{12}}{3^{3}r^{12}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{64n^{3}t^{12}}{27r^{12}}$$

Expand

$$\frac{64\times \left(\frac{t}{r}\right)^{12}n^{3}}{27}$$

Solution Steps

To raise \frac{4nt^{4}}{3r^{4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(4nt^{4}\right)^{3}}{\left(3r^{4}\right)^{3}}$$

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

$$\frac{4^{3}n^{3}\left(t^{4}\right)^{3}}{\left(3r^{4}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{4^{3}n^{3}t^{12}}{\left(3r^{4}\right)^{3}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{64n^{3}t^{12}}{\left(3r^{4}\right)^{3}}$$

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

$$\frac{64n^{3}t^{12}}{3^{3}\left(r^{4}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 3 to get 12.

$$\frac{64n^{3}t^{12}}{3^{3}r^{12}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{64n^{3}t^{12}}{27r^{12}}$$