Solve (v^{3}w^-1)(3u^-4v/w^-3)^3

$$( v ^ { 3 } w ^ { - 1 } ) ( \frac { 3 u ^ { - 4 } v } { w ^ { - 3 } } ) ^ { 3 }$$

Evaluate

$$\frac{27v^{6}w^{8}}{u^{12}}$$

Solution Steps

To raise \frac{3u^{-4}v}{w^{-3}} to a power, raise both numerator and denominator to the power and then divide.

$$v^{3}w^{-1}\times \frac{\left(3u^{-4}v\right)^{3}}{\left(w^{-3}\right)^{3}}$$

Express v^{3}\times \frac{\left(3u^{-4}v\right)^{3}}{\left(w^{-3}\right)^{3}} as a single fraction.

$$\frac{v^{3}\times \left(3u^{-4}v\right)^{3}}{\left(w^{-3}\right)^{3}}w^{-1}$$

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

$$\frac{v^{3}\times \left(3u^{-4}v\right)^{3}}{w^{-9}}w^{-1}$$

Expand \left(3u^{-4}v\right)^{3}.

$$\frac{v^{3}\times 3^{3}\left(u^{-4}\right)^{3}v^{3}}{w^{-9}}w^{-1}$$

To raise a power to another power, multiply the exponents. Multiply -4 and 3 to get -12.

$$\frac{v^{3}\times 3^{3}u^{-12}v^{3}}{w^{-9}}w^{-1}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{v^{3}\times 27u^{-12}v^{3}}{w^{-9}}w^{-1}$$

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

$$\frac{v^{6}\times 27u^{-12}}{w^{-9}}w^{-1}$$

Express \frac{v^{6}\times 27u^{-12}}{w^{-9}}w^{-1} as a single fraction.

$$\frac{v^{6}\times 27u^{-12}w^{-1}}{w^{-9}}$$

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

$$27u^{-12}v^{6}w^{8}$$

Expand

$$\frac{27v^{6}w^{8}}{u^{12}}$$

Solution Steps

To raise \frac{3u^{-4}v}{w^{-3}} to a power, raise both numerator and denominator to the power and then divide.

$$v^{3}w^{-1}\times \frac{\left(3u^{-4}v\right)^{3}}{\left(w^{-3}\right)^{3}}$$

Express v^{3}\times \frac{\left(3u^{-4}v\right)^{3}}{\left(w^{-3}\right)^{3}} as a single fraction.

$$\frac{v^{3}\times \left(3u^{-4}v\right)^{3}}{\left(w^{-3}\right)^{3}}w^{-1}$$

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

$$\frac{v^{3}\times \left(3u^{-4}v\right)^{3}}{w^{-9}}w^{-1}$$

Expand \left(3u^{-4}v\right)^{3}.

$$\frac{v^{3}\times 3^{3}\left(u^{-4}\right)^{3}v^{3}}{w^{-9}}w^{-1}$$

To raise a power to another power, multiply the exponents. Multiply -4 and 3 to get -12.

$$\frac{v^{3}\times 3^{3}u^{-12}v^{3}}{w^{-9}}w^{-1}$$

Calculate 3 to the power of 3 and get 27.

$$\frac{v^{3}\times 27u^{-12}v^{3}}{w^{-9}}w^{-1}$$

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

$$\frac{v^{6}\times 27u^{-12}}{w^{-9}}w^{-1}$$

Express \frac{v^{6}\times 27u^{-12}}{w^{-9}}w^{-1} as a single fraction.

$$\frac{v^{6}\times 27u^{-12}w^{-1}}{w^{-9}}$$

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

$$27u^{-12}v^{6}w^{8}$$