Solve ((frac{2u^{3}v^{-1}w^{0}}{3x^{-2}y^0z^3})^4)^-3

$$( ( \frac { 2 u ^ { 3 } v ^ { - 1 } w ^ { 0 } } { 3 x ^ { - 2 } y ^ { 0 } z ^ { 3 } } ) ^ { 4 } ) ^ { - 3 }$$

Evaluate

$$\frac{531441\times \left(\frac{z}{u}\right)^{36}v^{12}}{4096x^{24}}$$

Solution Steps

Calculate w to the power of 0 and get 1.

$$\left(\left(\frac{2u^{3}v^{-1}\times 1}{3x^{-2}y^{0}z^{3}}\right)^{4}\right)^{-3}$$

Multiply 2 and 1 to get 2.

$$\left(\left(\frac{2u^{3}v^{-1}}{3x^{-2}y^{0}z^{3}}\right)^{4}\right)^{-3}$$

Calculate y to the power of 0 and get 1.

$$\left(\left(\frac{2u^{3}v^{-1}}{3x^{-2}\times 1z^{3}}\right)^{4}\right)^{-3}$$

Multiply 3 and 1 to get 3.

$$\left(\left(\frac{2u^{3}v^{-1}}{3x^{-2}z^{3}}\right)^{4}\right)^{-3}$$

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

$$\left(\frac{\left(2u^{3}v^{-1}\right)^{4}}{\left(3x^{-2}z^{3}\right)^{4}}\right)^{-3}$$

To raise \frac{\left(2u^{3}v^{-1}\right)^{4}}{\left(3x^{-2}z^{3}\right)^{4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(\left(2u^{3}v^{-1}\right)^{4}\right)^{-3}}{\left(\left(3x^{-2}z^{3}\right)^{4}\right)^{-3}}$$

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

$$\frac{\left(2u^{3}v^{-1}\right)^{-12}}{\left(\left(3x^{-2}z^{3}\right)^{4}\right)^{-3}}$$

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

$$\frac{\left(2u^{3}v^{-1}\right)^{-12}}{\left(3x^{-2}z^{3}\right)^{-12}}$$

Expand \left(2u^{3}v^{-1}\right)^{-12}.

$$\frac{2^{-12}\left(u^{3}\right)^{-12}\left(v^{-1}\right)^{-12}}{\left(3x^{-2}z^{3}\right)^{-12}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -12 to get -36.

$$\frac{2^{-12}u^{-36}\left(v^{-1}\right)^{-12}}{\left(3x^{-2}z^{3}\right)^{-12}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and -12 to get 12.

$$\frac{2^{-12}u^{-36}v^{12}}{\left(3x^{-2}z^{3}\right)^{-12}}$$

Calculate 2 to the power of -12 and get \frac{1}{4096}.

$$\frac{\frac{1}{4096}u^{-36}v^{12}}{\left(3x^{-2}z^{3}\right)^{-12}}$$

Expand \left(3x^{-2}z^{3}\right)^{-12}.

$$\frac{\frac{1}{4096}u^{-36}v^{12}}{3^{-12}\left(x^{-2}\right)^{-12}\left(z^{3}\right)^{-12}}$$

To raise a power to another power, multiply the exponents. Multiply -2 and -12 to get 24.

$$\frac{\frac{1}{4096}u^{-36}v^{12}}{3^{-12}x^{24}\left(z^{3}\right)^{-12}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -12 to get -36.

$$\frac{\frac{1}{4096}u^{-36}v^{12}}{3^{-12}x^{24}z^{-36}}$$

Calculate 3 to the power of -12 and get \frac{1}{531441}.

$$\frac{\frac{1}{4096}u^{-36}v^{12}}{\frac{1}{531441}x^{24}z^{-36}}$$

Expand

$$\frac{531441\times \left(\frac{z}{u}\right)^{36}v^{12}}{4096x^{24}}$$

Solution Steps

Calculate w to the power of 0 and get 1.

$$\left(\left(\frac{2u^{3}v^{-1}\times 1}{3x^{-2}y^{0}z^{3}}\right)^{4}\right)^{-3}$$

Multiply 2 and 1 to get 2.

$$\left(\left(\frac{2u^{3}v^{-1}}{3x^{-2}y^{0}z^{3}}\right)^{4}\right)^{-3}$$

Calculate y to the power of 0 and get 1.

$$\left(\left(\frac{2u^{3}v^{-1}}{3x^{-2}\times 1z^{3}}\right)^{4}\right)^{-3}$$

Multiply 3 and 1 to get 3.

$$\left(\left(\frac{2u^{3}v^{-1}}{3x^{-2}z^{3}}\right)^{4}\right)^{-3}$$

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

$$\left(\frac{\left(2u^{3}v^{-1}\right)^{4}}{\left(3x^{-2}z^{3}\right)^{4}}\right)^{-3}$$

To raise \frac{\left(2u^{3}v^{-1}\right)^{4}}{\left(3x^{-2}z^{3}\right)^{4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{\left(\left(2u^{3}v^{-1}\right)^{4}\right)^{-3}}{\left(\left(3x^{-2}z^{3}\right)^{4}\right)^{-3}}$$

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

$$\frac{\left(2u^{3}v^{-1}\right)^{-12}}{\left(\left(3x^{-2}z^{3}\right)^{4}\right)^{-3}}$$

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

$$\frac{\left(2u^{3}v^{-1}\right)^{-12}}{\left(3x^{-2}z^{3}\right)^{-12}}$$

Expand \left(2u^{3}v^{-1}\right)^{-12}.

$$\frac{2^{-12}\left(u^{3}\right)^{-12}\left(v^{-1}\right)^{-12}}{\left(3x^{-2}z^{3}\right)^{-12}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -12 to get -36.

$$\frac{2^{-12}u^{-36}\left(v^{-1}\right)^{-12}}{\left(3x^{-2}z^{3}\right)^{-12}}$$

To raise a power to another power, multiply the exponents. Multiply -1 and -12 to get 12.

$$\frac{2^{-12}u^{-36}v^{12}}{\left(3x^{-2}z^{3}\right)^{-12}}$$

Calculate 2 to the power of -12 and get \frac{1}{4096}.

$$\frac{\frac{1}{4096}u^{-36}v^{12}}{\left(3x^{-2}z^{3}\right)^{-12}}$$

Expand \left(3x^{-2}z^{3}\right)^{-12}.

$$\frac{\frac{1}{4096}u^{-36}v^{12}}{3^{-12}\left(x^{-2}\right)^{-12}\left(z^{3}\right)^{-12}}$$

To raise a power to another power, multiply the exponents. Multiply -2 and -12 to get 24.

$$\frac{\frac{1}{4096}u^{-36}v^{12}}{3^{-12}x^{24}\left(z^{3}\right)^{-12}}$$

To raise a power to another power, multiply the exponents. Multiply 3 and -12 to get -36.

$$\frac{\frac{1}{4096}u^{-36}v^{12}}{3^{-12}x^{24}z^{-36}}$$

Calculate 3 to the power of -12 and get \frac{1}{531441}.

$$\frac{\frac{1}{4096}u^{-36}v^{12}}{\frac{1}{531441}x^{24}z^{-36}}$$