Solve (frac{xu^{-2}}{3z^-2})^3(x^3z^-1)

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

Evaluate

$$\frac{\left(\frac{x}{u}\right)^{6}z^{5}}{27}$$

Solution Steps

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

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

Express \frac{\left(xu^{-2}\right)^{3}}{\left(3z^{-2}\right)^{3}}x^{3} as a single fraction.

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

Express \frac{\left(xu^{-2}\right)^{3}x^{3}}{\left(3z^{-2}\right)^{3}}z^{-1} as a single fraction.

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

Expand \left(xu^{-2}\right)^{3}.

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

To raise a power to another power, multiply the exponents. Multiply -2 and 3 to get -6.

$$\frac{x^{3}u^{-6}x^{3}z^{-1}}{\left(3z^{-2}\right)^{3}}$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$\frac{x^{6}u^{-6}z^{-1}}{\left(3z^{-2}\right)^{3}}$$

Expand \left(3z^{-2}\right)^{3}.

$$\frac{x^{6}u^{-6}z^{-1}}{3^{3}\left(z^{-2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply -2 and 3 to get -6.

$$\frac{x^{6}u^{-6}z^{-1}}{3^{3}z^{-6}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{x^{6}u^{-6}z^{-1}}{27z^{-6}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{u^{-6}z^{5}x^{6}}{27}$$

Expand

$$\frac{\left(\frac{x}{u}\right)^{6}z^{5}}{27}$$

Solution Steps

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

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

Express \frac{\left(xu^{-2}\right)^{3}}{\left(3z^{-2}\right)^{3}}x^{3} as a single fraction.

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

Express \frac{\left(xu^{-2}\right)^{3}x^{3}}{\left(3z^{-2}\right)^{3}}z^{-1} as a single fraction.

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

Expand \left(xu^{-2}\right)^{3}.

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

To raise a power to another power, multiply the exponents. Multiply -2 and 3 to get -6.

$$\frac{x^{3}u^{-6}x^{3}z^{-1}}{\left(3z^{-2}\right)^{3}}$$

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$\frac{x^{6}u^{-6}z^{-1}}{\left(3z^{-2}\right)^{3}}$$

Expand \left(3z^{-2}\right)^{3}.

$$\frac{x^{6}u^{-6}z^{-1}}{3^{3}\left(z^{-2}\right)^{3}}$$

To raise a power to another power, multiply the exponents. Multiply -2 and 3 to get -6.

$$\frac{x^{6}u^{-6}z^{-1}}{3^{3}z^{-6}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{x^{6}u^{-6}z^{-1}}{27z^{-6}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{u^{-6}z^{5}x^{6}}{27}$$