Solve (4w^6x^9/z^6)^3

$$( \frac { 4 w ^ { 6 } x ^ { 9 } } { z ^ { 6 } } ) ^ { 3 }$$

Evaluate

$$64\times \left(\frac{w}{z}\right)^{18}x^{27}$$

Solution Steps

To raise \frac{4w^{6}x^{9}}{z^{6}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(4w^{6}x^{9}\right)^{3}}{\left(z^{6}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 3 to get 18.

$$\frac{\left(4w^{6}x^{9}\right)^{3}}{z^{18}}$$

Expand \left(4w^{6}x^{9}\right)^{3}.

$$\frac{4^{3}\left(w^{6}\right)^{3}\left(x^{9}\right)^{3}}{z^{18}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 3 to get 18.

$$\frac{4^{3}w^{18}\left(x^{9}\right)^{3}}{z^{18}}$$

To raise a power to another power, multiply the exponents. Multiply 9 and 3 to get 27.

$$\frac{4^{3}w^{18}x^{27}}{z^{18}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{64w^{18}x^{27}}{z^{18}}$$

Expand

$$64\times \left(\frac{w}{z}\right)^{18}x^{27}$$

Solution Steps

To raise \frac{4w^{6}x^{9}}{z^{6}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(4w^{6}x^{9}\right)^{3}}{\left(z^{6}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 3 to get 18.

$$\frac{\left(4w^{6}x^{9}\right)^{3}}{z^{18}}$$

Expand \left(4w^{6}x^{9}\right)^{3}.

$$\frac{4^{3}\left(w^{6}\right)^{3}\left(x^{9}\right)^{3}}{z^{18}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 3 to get 18.

$$\frac{4^{3}w^{18}\left(x^{9}\right)^{3}}{z^{18}}$$

To raise a power to another power, multiply the exponents. Multiply 9 and 3 to get 27.

$$\frac{4^{3}w^{18}x^{27}}{z^{18}}$$

Calculate 4 to the power of 3 and get 64.

$$\frac{64w^{18}x^{27}}{z^{18}}$$