Solve (2x^-3y^7/z^-1)^3

$$( \frac { 2 x ^ { - 3 } y ^ { 7 } } { z ^ { - 1 } } ) ^ { 3 }$$

Evaluate

$$\frac{8z^{3}y^{21}}{x^{9}}$$

Solution Steps

To raise \frac{2x^{-3}y^{7}}{z^{-1}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2x^{-3}y^{7}\right)^{3}}{\left(z^{-1}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 3 to get -3.

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

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

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

To raise a power to another power, multiply the exponents. Multiply -3 and 3 to get -9.

$$\frac{2^{3}x^{-9}\left(y^{7}\right)^{3}}{z^{-3}}$$

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

$$\frac{2^{3}x^{-9}y^{21}}{z^{-3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{8x^{-9}y^{21}}{z^{-3}}$$

Expand

$$\frac{8z^{3}y^{21}}{x^{9}}$$

Solution Steps

To raise \frac{2x^{-3}y^{7}}{z^{-1}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(2x^{-3}y^{7}\right)^{3}}{\left(z^{-1}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 3 to get -3.

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

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

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

To raise a power to another power, multiply the exponents. Multiply -3 and 3 to get -9.

$$\frac{2^{3}x^{-9}\left(y^{7}\right)^{3}}{z^{-3}}$$

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

$$\frac{2^{3}x^{-9}y^{21}}{z^{-3}}$$

Calculate 2 to the power of 3 and get 8.

$$\frac{8x^{-9}y^{21}}{z^{-3}}$$