Solve (-3x^5/y^6)^2

$$( - \frac { 3 x ^ { 5 } } { y ^ { 6 } } ) ^ { 2 }$$

Evaluate

$$\frac{9x^{10}}{y^{12}}$$

Solution Steps

Calculate -\frac{3x^{5}}{y^{6}} to the power of 2 and get \left(\frac{3x^{5}}{y^{6}}\right)^{2}.

$$\left(\frac{3x^{5}}{y^{6}}\right)^{2}$$

To raise \frac{3x^{5}}{y^{6}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(3x^{5}\right)^{2}}{\left(y^{6}\right)^{2}}$$

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

$$\frac{\left(3x^{5}\right)^{2}}{y^{12}}$$

Expand \left(3x^{5}\right)^{2}.

$$\frac{3^{2}\left(x^{5}\right)^{2}}{y^{12}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{3^{2}x^{10}}{y^{12}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9x^{10}}{y^{12}}$$

Expand

$$\frac{9x^{10}}{y^{12}}$$

Solution Steps

Calculate -\frac{3x^{5}}{y^{6}} to the power of 2 and get \left(\frac{3x^{5}}{y^{6}}\right)^{2}.

$$\left(\frac{3x^{5}}{y^{6}}\right)^{2}$$

To raise \frac{3x^{5}}{y^{6}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(3x^{5}\right)^{2}}{\left(y^{6}\right)^{2}}$$

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

$$\frac{\left(3x^{5}\right)^{2}}{y^{12}}$$

Expand \left(3x^{5}\right)^{2}.

$$\frac{3^{2}\left(x^{5}\right)^{2}}{y^{12}}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{3^{2}x^{10}}{y^{12}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{9x^{10}}{y^{12}}$$