Solve (-x^-2y^3z^-4)^-7

$$( - x ^ { - 2 } y ^ { 3 } z ^ { - 4 } ) ^ { - 7 }$$

Evaluate

$$-\frac{x^{14}z^{28}}{y^{21}}$$

Solution Steps

Expand \left(\left(-x^{-2}\right)y^{3}z^{-4}\right)^{-7}.

$$\left(-x^{-2}\right)^{-7}\left(y^{3}\right)^{-7}\left(z^{-4}\right)^{-7}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -7 to get -21.

$$\left(-x^{-2}\right)^{-7}y^{-21}\left(z^{-4}\right)^{-7}$$

To raise a power to another power, multiply the exponents. Multiply -4 and -7 to get 28.

$$\left(-x^{-2}\right)^{-7}y^{-21}z^{28}$$

Expand \left(-x^{-2}\right)^{-7}.

$$\left(-1\right)^{-7}\left(x^{-2}\right)^{-7}y^{-21}z^{28}$$

To raise a power to another power, multiply the exponents. Multiply -2 and -7 to get 14.

$$\left(-1\right)^{-7}x^{14}y^{-21}z^{28}$$

Calculate -1 to the power of -7 and get -1.

$$-x^{14}y^{-21}z^{28}$$

Expand

$$-\frac{x^{14}z^{28}}{y^{21}}$$

Solution Steps

Expand \left(\left(-x^{-2}\right)y^{3}z^{-4}\right)^{-7}.

$$\left(-x^{-2}\right)^{-7}\left(y^{3}\right)^{-7}\left(z^{-4}\right)^{-7}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -7 to get -21.

$$\left(-x^{-2}\right)^{-7}y^{-21}\left(z^{-4}\right)^{-7}$$

To raise a power to another power, multiply the exponents. Multiply -4 and -7 to get 28.

$$\left(-x^{-2}\right)^{-7}y^{-21}z^{28}$$

Expand \left(-x^{-2}\right)^{-7}.

$$\left(-1\right)^{-7}\left(x^{-2}\right)^{-7}y^{-21}z^{28}$$

To raise a power to another power, multiply the exponents. Multiply -2 and -7 to get 14.

$$\left(-1\right)^{-7}x^{14}y^{-21}z^{28}$$

Calculate -1 to the power of -7 and get -1.

$$-x^{14}y^{-21}z^{28}$$