Solve (-x^5y^7)^6

$$( - x ^ { 5 } y ^ { 7 } ) ^ { 6 }$$

Evaluate

$$x^{30}y^{42}$$

Solution Steps

Expand \left(\left(-x^{5}\right)y^{7}\right)^{6}.

$$\left(-x^{5}\right)^{6}\left(y^{7}\right)^{6}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 6 to get 42.

$$\left(-x^{5}\right)^{6}y^{42}$$

Expand \left(-x^{5}\right)^{6}.

$$\left(-1\right)^{6}\left(x^{5}\right)^{6}y^{42}$$

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

$$\left(-1\right)^{6}x^{30}y^{42}$$

Calculate -1 to the power of 6 and get 1.

$$1x^{30}y^{42}$$

For any term t, t\times 1=t and 1t=t.

$$x^{30}y^{42}$$

Expand

$$x^{30}y^{42}$$

Solution Steps

Expand \left(\left(-x^{5}\right)y^{7}\right)^{6}.

$$\left(-x^{5}\right)^{6}\left(y^{7}\right)^{6}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 6 to get 42.

$$\left(-x^{5}\right)^{6}y^{42}$$

Expand \left(-x^{5}\right)^{6}.

$$\left(-1\right)^{6}\left(x^{5}\right)^{6}y^{42}$$

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

$$\left(-1\right)^{6}x^{30}y^{42}$$

Calculate -1 to the power of 6 and get 1.

$$1x^{30}y^{42}$$

For any term t, t\times 1=t and 1t=t.

$$x^{30}y^{42}$$