Solve {left(3^3/2x^6y^4right)}^4

$${ \left( \frac{ { 3 }^{ 3 } }{ 2 { x }^{ 6 } { y }^{ 4 } } \right) }^{ 4 }$$

Evaluate

$$\frac{531441}{16y^{16}x^{24}}$$

Solution Steps

Calculate 3 to the power of 3 and get 27.

$$\left(\frac{27}{2x^{6}y^{4}}\right)^{4}$$

To raise \frac{27}{2x^{6}y^{4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{27^{4}}{\left(2x^{6}y^{4}\right)^{4}}$$

Calculate 27 to the power of 4 and get 531441.

$$\frac{531441}{\left(2x^{6}y^{4}\right)^{4}}$$

Expand \left(2x^{6}y^{4}\right)^{4}.

$$\frac{531441}{2^{4}\left(x^{6}\right)^{4}\left(y^{4}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 4 to get 24.

$$\frac{531441}{2^{4}x^{24}\left(y^{4}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$\frac{531441}{2^{4}x^{24}y^{16}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{531441}{16x^{24}y^{16}}$$

Expand

$$\frac{531441}{16y^{16}x^{24}}$$

Solution Steps

Calculate 3 to the power of 3 and get 27.

$$\left(\frac{27}{2x^{6}y^{4}}\right)^{4}$$

To raise \frac{27}{2x^{6}y^{4}} to a power, raise both numerator and denominator to the power and then divide.

$$\frac{27^{4}}{\left(2x^{6}y^{4}\right)^{4}}$$

Calculate 27 to the power of 4 and get 531441.

$$\frac{531441}{\left(2x^{6}y^{4}\right)^{4}}$$

Expand \left(2x^{6}y^{4}\right)^{4}.

$$\frac{531441}{2^{4}\left(x^{6}\right)^{4}\left(y^{4}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 4 to get 24.

$$\frac{531441}{2^{4}x^{24}\left(y^{4}\right)^{4}}$$

To raise a power to another power, multiply the exponents. Multiply 4 and 4 to get 16.

$$\frac{531441}{2^{4}x^{24}y^{16}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{531441}{16x^{24}y^{16}}$$