Solve (-x^3y^5z^7)^5

$$( - x ^ { 3 } y ^ { 5 } z ^ { 7 } ) ^ { 5 }$$

Evaluate

$$-x^{15}y^{25}z^{35}$$

Solution Steps

Expand \left(\left(-x^{3}\right)y^{5}z^{7}\right)^{5}.

$$\left(-x^{3}\right)^{5}\left(y^{5}\right)^{5}\left(z^{7}\right)^{5}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 5 to get 25.

$$\left(-x^{3}\right)^{5}y^{25}\left(z^{7}\right)^{5}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 5 to get 35.

$$\left(-x^{3}\right)^{5}y^{25}z^{35}$$

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

$$\left(-1\right)^{5}\left(x^{3}\right)^{5}y^{25}z^{35}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 5 to get 15.

$$\left(-1\right)^{5}x^{15}y^{25}z^{35}$$

Calculate -1 to the power of 5 and get -1.

$$-x^{15}y^{25}z^{35}$$

Expand

$$-x^{15}y^{25}z^{35}$$

Solution Steps

Expand \left(\left(-x^{3}\right)y^{5}z^{7}\right)^{5}.

$$\left(-x^{3}\right)^{5}\left(y^{5}\right)^{5}\left(z^{7}\right)^{5}$$

To raise a power to another power, multiply the exponents. Multiply 5 and 5 to get 25.

$$\left(-x^{3}\right)^{5}y^{25}\left(z^{7}\right)^{5}$$

To raise a power to another power, multiply the exponents. Multiply 7 and 5 to get 35.

$$\left(-x^{3}\right)^{5}y^{25}z^{35}$$

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

$$\left(-1\right)^{5}\left(x^{3}\right)^{5}y^{25}z^{35}$$

To raise a power to another power, multiply the exponents. Multiply 3 and 5 to get 15.

$$\left(-1\right)^{5}x^{15}y^{25}z^{35}$$

Calculate -1 to the power of 5 and get -1.

$$-x^{15}y^{25}z^{35}$$