Solve (3x^{3}y^2div2y^2z^3)^4

$$( 3 x ^ { 3 } y ^ { 2 } \div 2 y ^ { 2 } z ^ { 3 } ) ^ { 4 }$$

Evaluate

$$\frac{81y^{16}\left(xz\right)^{12}}{16}$$

Solution Steps

Express \frac{3x^{3}y^{2}}{2}y^{2} as a single fraction.

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

Express \frac{3x^{3}y^{2}y^{2}}{2}z^{3} as a single fraction.

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

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

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

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

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

Expand \left(3x^{3}y^{4}z^{3}\right)^{4}.

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

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

$$\frac{3^{4}x^{12}\left(y^{4}\right)^{4}\left(z^{3}\right)^{4}}{2^{4}}$$

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

$$\frac{3^{4}x^{12}y^{16}\left(z^{3}\right)^{4}}{2^{4}}$$

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

$$\frac{3^{4}x^{12}y^{16}z^{12}}{2^{4}}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{81x^{12}y^{16}z^{12}}{2^{4}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{81x^{12}y^{16}z^{12}}{16}$$

Expand

$$\frac{81y^{16}\left(xz\right)^{12}}{16}$$

Solution Steps

Express \frac{3x^{3}y^{2}}{2}y^{2} as a single fraction.

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

Express \frac{3x^{3}y^{2}y^{2}}{2}z^{3} as a single fraction.

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

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

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

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

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

Expand \left(3x^{3}y^{4}z^{3}\right)^{4}.

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

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

$$\frac{3^{4}x^{12}\left(y^{4}\right)^{4}\left(z^{3}\right)^{4}}{2^{4}}$$

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

$$\frac{3^{4}x^{12}y^{16}\left(z^{3}\right)^{4}}{2^{4}}$$

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

$$\frac{3^{4}x^{12}y^{16}z^{12}}{2^{4}}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{81x^{12}y^{16}z^{12}}{2^{4}}$$

Calculate 2 to the power of 4 and get 16.

$$\frac{81x^{12}y^{16}z^{12}}{16}$$