Solve [2x^4/6z^8]^3

$$[ \frac { 2 x ^ { 4 } } { 6 z ^ { 8 } } ] ^ { 3 }$$

Evaluate

$$\frac{x^{12}}{27z^{24}}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\left(\frac{x^{4}}{3z^{8}}\right)^{3}$$

To raise \frac{x^{4}}{3z^{8}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(x^{4}\right)^{3}}{\left(3z^{8}\right)^{3}}$$

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

$$\frac{x^{12}}{\left(3z^{8}\right)^{3}}$$

Expand \left(3z^{8}\right)^{3}.

$$\frac{x^{12}}{3^{3}\left(z^{8}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 3 to get 24.

$$\frac{x^{12}}{3^{3}z^{24}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{x^{12}}{27z^{24}}$$

Expand

$$\frac{x^{12}}{27z^{24}}$$

Solution Steps

Cancel out 2 in both numerator and denominator.

$$\left(\frac{x^{4}}{3z^{8}}\right)^{3}$$

To raise \frac{x^{4}}{3z^{8}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(x^{4}\right)^{3}}{\left(3z^{8}\right)^{3}}$$

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

$$\frac{x^{12}}{\left(3z^{8}\right)^{3}}$$

Expand \left(3z^{8}\right)^{3}.

$$\frac{x^{12}}{3^{3}\left(z^{8}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply 8 and 3 to get 24.

$$\frac{x^{12}}{3^{3}z^{24}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{x^{12}}{27z^{24}}$$