Solve (4x^3y^4/z^4)^3

$$( \frac { 4 x ^ { 3 } y ^ { 4 } } { z ^ { 4 } } ) ^ { 3 }$$

Evaluate

$$64\times \left(\frac{y}{z}\right)^{12}x^{9}$$

Solution Steps

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

$$\frac{\left(4x^{3}y^{4}\right)^{3}}{\left(z^{4}\right)^{3}}$$

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

$$\frac{\left(4x^{3}y^{4}\right)^{3}}{z^{12}}$$

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

$$\frac{4^{3}\left(x^{3}\right)^{3}\left(y^{4}\right)^{3}}{z^{12}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{4^{3}x^{9}\left(y^{4}\right)^{3}}{z^{12}}$$

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

$$\frac{4^{3}x^{9}y^{12}}{z^{12}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{64x^{9}y^{12}}{z^{12}}$$

Expand

$$64\times \left(\frac{y}{z}\right)^{12}x^{9}$$

Solution Steps

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

$$\frac{\left(4x^{3}y^{4}\right)^{3}}{\left(z^{4}\right)^{3}}$$

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

$$\frac{\left(4x^{3}y^{4}\right)^{3}}{z^{12}}$$

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

$$\frac{4^{3}\left(x^{3}\right)^{3}\left(y^{4}\right)^{3}}{z^{12}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 3 to get 9.

$$\frac{4^{3}x^{9}\left(y^{4}\right)^{3}}{z^{12}}$$

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

$$\frac{4^{3}x^{9}y^{12}}{z^{12}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{64x^{9}y^{12}}{z^{12}}$$