Solve left(y^8divy^10right)^6

$${ \left( { y }^{ 8 } \div { y }^{ 10 } \right) }^{ 6 }$$

Evaluate

$$\frac{1}{y^{12}}$$

Solution Steps

Rewrite y^{10} as y^{8}y^{2}. Cancel out y^{8} in both numerator and denominator.

$$\left(\frac{1}{y^{2}}\right)^{6}$$

To raise \frac{1}{y^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1^{6}}{\left(y^{2}\right)^{6}}$$

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

$$\frac{1^{6}}{y^{12}}$$

Calculate 1 to the power of 6 and get 1.

$$\frac{1}{y^{12}}$$

Expand

$$\frac{1}{y^{12}}$$

Solution Steps

Rewrite y^{10} as y^{8}y^{2}. Cancel out y^{8} in both numerator and denominator.

$$\left(\frac{1}{y^{2}}\right)^{6}$$

To raise \frac{1}{y^{2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{1^{6}}{\left(y^{2}\right)^{6}}$$

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

$$\frac{1^{6}}{y^{12}}$$

Calculate 1 to the power of 6 and get 1.

$$\frac{1}{y^{12}}$$