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

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

Evaluate

$$\frac{z^{6}x^{9}}{27}$$

Solution Steps

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

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

Multiply \frac{u^{3}}{z^{3}} times \frac{\left(x^{3}u^{-1}\right)^{3}}{\left(3z^{-3}\right)^{3}} by multiplying numerator times numerator and denominator times denominator.

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

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

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

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

$$\frac{u^{3}x^{9}\left(u^{-1}\right)^{3}}{z^{3}\times \left(3z^{-3}\right)^{3}}$$

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

$$\frac{u^{3}x^{9}u^{-3}}{z^{3}\times \left(3z^{-3}\right)^{3}}$$

Multiply u^{3} and u^{-3} to get 1.

$$\frac{x^{9}}{z^{3}\times \left(3z^{-3}\right)^{3}}$$

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

$$\frac{x^{9}}{z^{3}\times 3^{3}\left(z^{-3}\right)^{3}}$$

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

$$\frac{x^{9}}{z^{3}\times 3^{3}z^{-9}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{x^{9}}{z^{3}\times 27z^{-9}}$$

To multiply powers of the same base, add their exponents. Add 3 and -9 to get -6.

$$\frac{x^{9}}{z^{-6}\times 27}$$

Expand

$$\frac{z^{6}x^{9}}{27}$$

Solution Steps

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

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

Multiply \frac{u^{3}}{z^{3}} times \frac{\left(x^{3}u^{-1}\right)^{3}}{\left(3z^{-3}\right)^{3}} by multiplying numerator times numerator and denominator times denominator.

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

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

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

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

$$\frac{u^{3}x^{9}\left(u^{-1}\right)^{3}}{z^{3}\times \left(3z^{-3}\right)^{3}}$$

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

$$\frac{u^{3}x^{9}u^{-3}}{z^{3}\times \left(3z^{-3}\right)^{3}}$$

Multiply u^{3} and u^{-3} to get 1.

$$\frac{x^{9}}{z^{3}\times \left(3z^{-3}\right)^{3}}$$

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

$$\frac{x^{9}}{z^{3}\times 3^{3}\left(z^{-3}\right)^{3}}$$

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

$$\frac{x^{9}}{z^{3}\times 3^{3}z^{-9}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{x^{9}}{z^{3}\times 27z^{-9}}$$

To multiply powers of the same base, add their exponents. Add 3 and -9 to get -6.

$$\frac{x^{9}}{z^{-6}\times 27}$$