Solve (frac{3uv^{-4}}{w^-2})^3(v^3w^-1)

$$( \frac { 3 u v ^ { - 4 } } { w ^ { - 2 } } ) ^ { 3 } ( v ^ { 3 } w ^ { - 1 } )$$

Evaluate

$$\frac{27u^{3}w^{5}}{v^{9}}$$

Solution Steps

To raise \frac{3uv^{-4}}{w^{-2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(3uv^{-4}\right)^{3}}{\left(w^{-2}\right)^{3}}v^{3}w^{-1}$$

Express \frac{\left(3uv^{-4}\right)^{3}}{\left(w^{-2}\right)^{3}}v^{3} as a single fraction.

$$\frac{\left(3uv^{-4}\right)^{3}v^{3}}{\left(w^{-2}\right)^{3}}w^{-1}$$

Express \frac{\left(3uv^{-4}\right)^{3}v^{3}}{\left(w^{-2}\right)^{3}}w^{-1} as a single fraction.

$$\frac{\left(3uv^{-4}\right)^{3}v^{3}w^{-1}}{\left(w^{-2}\right)^{3}}$$

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

$$\frac{\left(3uv^{-4}\right)^{3}v^{3}w^{-1}}{w^{-6}}$$

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

$$\left(3v^{-4}u\right)^{3}v^{3}w^{5}$$

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

$$3^{3}\left(v^{-4}\right)^{3}u^{3}v^{3}w^{5}$$

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

$$3^{3}v^{-12}u^{3}v^{3}w^{5}$$

Calculate 3 to the power of 3 and get 27.

$$27v^{-12}u^{3}v^{3}w^{5}$$

To multiply powers of the same base, add their exponents. Add -12 and 3 to get -9.

$$27v^{-9}u^{3}w^{5}$$

Expand

$$\frac{27u^{3}w^{5}}{v^{9}}$$

Solution Steps

To raise \frac{3uv^{-4}}{w^{-2}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(3uv^{-4}\right)^{3}}{\left(w^{-2}\right)^{3}}v^{3}w^{-1}$$

Express \frac{\left(3uv^{-4}\right)^{3}}{\left(w^{-2}\right)^{3}}v^{3} as a single fraction.

$$\frac{\left(3uv^{-4}\right)^{3}v^{3}}{\left(w^{-2}\right)^{3}}w^{-1}$$

Express \frac{\left(3uv^{-4}\right)^{3}v^{3}}{\left(w^{-2}\right)^{3}}w^{-1} as a single fraction.

$$\frac{\left(3uv^{-4}\right)^{3}v^{3}w^{-1}}{\left(w^{-2}\right)^{3}}$$

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

$$\frac{\left(3uv^{-4}\right)^{3}v^{3}w^{-1}}{w^{-6}}$$

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

$$\left(3v^{-4}u\right)^{3}v^{3}w^{5}$$

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

$$3^{3}\left(v^{-4}\right)^{3}u^{3}v^{3}w^{5}$$

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

$$3^{3}v^{-12}u^{3}v^{3}w^{5}$$

Calculate 3 to the power of 3 and get 27.

$$27v^{-12}u^{3}v^{3}w^{5}$$

To multiply powers of the same base, add their exponents. Add -12 and 3 to get -9.

$$27v^{-9}u^{3}w^{5}$$