Solve (frac{3u^{-1}v^{3}}{w^-3})^3(u^3/w^3)

$$( \frac { 3 u ^ { - 1 } v ^ { 3 } } { w ^ { - 3 } } ) ^ { 3 } ( \frac { u ^ { 3 } } { w ^ { 3 } } )$$

Evaluate

$$27w^{6}v^{9}$$

Solution Steps

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

$$\frac{\left(3u^{-1}v^{3}\right)^{3}}{\left(w^{-3}\right)^{3}}\times \frac{u^{3}}{w^{3}}$$

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

$$\frac{\left(3u^{-1}v^{3}\right)^{3}u^{3}}{\left(w^{-3}\right)^{3}w^{3}}$$

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

$$\frac{\left(3u^{-1}v^{3}\right)^{3}u^{3}}{w^{-9}w^{3}}$$

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

$$\frac{\left(3u^{-1}v^{3}\right)^{3}u^{3}}{w^{-6}}$$

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

$$\frac{3^{3}\left(u^{-1}\right)^{3}\left(v^{3}\right)^{3}u^{3}}{w^{-6}}$$

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

$$\frac{3^{3}u^{-3}\left(v^{3}\right)^{3}u^{3}}{w^{-6}}$$

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

$$\frac{3^{3}u^{-3}v^{9}u^{3}}{w^{-6}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{27u^{-3}v^{9}u^{3}}{w^{-6}}$$

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

$$\frac{27v^{9}}{w^{-6}}$$

Expand

$$27w^{6}v^{9}$$

Solution Steps

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

$$\frac{\left(3u^{-1}v^{3}\right)^{3}}{\left(w^{-3}\right)^{3}}\times \frac{u^{3}}{w^{3}}$$

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

$$\frac{\left(3u^{-1}v^{3}\right)^{3}u^{3}}{\left(w^{-3}\right)^{3}w^{3}}$$

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

$$\frac{\left(3u^{-1}v^{3}\right)^{3}u^{3}}{w^{-9}w^{3}}$$

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

$$\frac{\left(3u^{-1}v^{3}\right)^{3}u^{3}}{w^{-6}}$$

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

$$\frac{3^{3}\left(u^{-1}\right)^{3}\left(v^{3}\right)^{3}u^{3}}{w^{-6}}$$

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

$$\frac{3^{3}u^{-3}\left(v^{3}\right)^{3}u^{3}}{w^{-6}}$$

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

$$\frac{3^{3}u^{-3}v^{9}u^{3}}{w^{-6}}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{27u^{-3}v^{9}u^{3}}{w^{-6}}$$

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

$$\frac{27v^{9}}{w^{-6}}$$