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

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

Evaluate

$$\frac{27u^{4}z^{8}}{x^{6}}$$

Solution Steps

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

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

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

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

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

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

Expand \left(x^{2}u^{-1}\right)^{-3}.

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

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

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

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

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

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{x^{-6}u^{4}z^{2}}{\left(3z^{2}\right)^{-3}}$$

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

$$\frac{x^{-6}u^{4}z^{2}}{3^{-3}\left(z^{2}\right)^{-3}}$$

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

$$\frac{x^{-6}u^{4}z^{2}}{3^{-3}z^{-6}}$$

Calculate 3 to the power of -3 and get \frac{1}{27}.

$$\frac{x^{-6}u^{4}z^{2}}{\frac{1}{27}z^{-6}}$$

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

$$\frac{x^{-6}u^{4}z^{8}}{\frac{1}{27}}$$

Divide x^{-6}u^{4}z^{8} by \frac{1}{27} by multiplying x^{-6}u^{4}z^{8} by the reciprocal of \frac{1}{27}.

$$x^{-6}u^{4}z^{8}\times 27$$

Expand

$$\frac{27u^{4}z^{8}}{x^{6}}$$

Solution Steps

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

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

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

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

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

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

Expand \left(x^{2}u^{-1}\right)^{-3}.

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

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

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

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

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

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{x^{-6}u^{4}z^{2}}{\left(3z^{2}\right)^{-3}}$$

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

$$\frac{x^{-6}u^{4}z^{2}}{3^{-3}\left(z^{2}\right)^{-3}}$$

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

$$\frac{x^{-6}u^{4}z^{2}}{3^{-3}z^{-6}}$$

Calculate 3 to the power of -3 and get \frac{1}{27}.

$$\frac{x^{-6}u^{4}z^{2}}{\frac{1}{27}z^{-6}}$$

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

$$\frac{x^{-6}u^{4}z^{8}}{\frac{1}{27}}$$

Divide x^{-6}u^{4}z^{8} by \frac{1}{27} by multiplying x^{-6}u^{4}z^{8} by the reciprocal of \frac{1}{27}.

$$x^{-6}u^{4}z^{8}\times 27$$