Solve (4y^5/8z^2)^6

$$( \frac { 4 y ^ { 5 } } { 8 z ^ { 2 } } ) ^ { 6 }$$

Evaluate

$$\frac{y^{30}}{64z^{12}}$$

Solution Steps

Cancel out 4 in both numerator and denominator.

$$\left(\frac{y^{5}}{2z^{2}}\right)^{6}$$

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

$$\frac{\left(y^{5}\right)^{6}}{\left(2z^{2}\right)^{6}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 6 to get 30.

$$\frac{y^{30}}{\left(2z^{2}\right)^{6}}$$

Expand \left(2z^{2}\right)^{6}.

$$\frac{y^{30}}{2^{6}\left(z^{2}\right)^{6}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 6 to get 12.

$$\frac{y^{30}}{2^{6}z^{12}}$$

Calculate 2 to the power of 6 and get 64.

$$\frac{y^{30}}{64z^{12}}$$

Expand

$$\frac{y^{30}}{64z^{12}}$$

Solution Steps

Cancel out 4 in both numerator and denominator.

$$\left(\frac{y^{5}}{2z^{2}}\right)^{6}$$

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

$$\frac{\left(y^{5}\right)^{6}}{\left(2z^{2}\right)^{6}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 6 to get 30.

$$\frac{y^{30}}{\left(2z^{2}\right)^{6}}$$

Expand \left(2z^{2}\right)^{6}.

$$\frac{y^{30}}{2^{6}\left(z^{2}\right)^{6}}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 6 to get 12.

$$\frac{y^{30}}{2^{6}z^{12}}$$

Calculate 2 to the power of 6 and get 64.

$$\frac{y^{30}}{64z^{12}}$$