Solve [(1/2x^2y^3)^3]^2

$$[ ( \frac { 1 } { 2 } x ^ { 2 } y ^ { 3 } ) ^ { 3 } ] ^ { 2 }$$

Evaluate

$$\frac{x^{12}y^{18}}{64}$$

Solution Steps

Expand \left(\frac{1}{2}x^{2}y^{3}\right)^{3}.

$$\left(\left(\frac{1}{2}\right)^{3}\left(x^{2}\right)^{3}\left(y^{3}\right)^{3}\right)^{2}$$

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

$$\left(\left(\frac{1}{2}\right)^{3}x^{6}\left(y^{3}\right)^{3}\right)^{2}$$

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

$$\left(\left(\frac{1}{2}\right)^{3}x^{6}y^{9}\right)^{2}$$

Calculate \frac{1}{2} to the power of 3 and get \frac{1}{8}.

$$\left(\frac{1}{8}x^{6}y^{9}\right)^{2}$$

Expand \left(\frac{1}{8}x^{6}y^{9}\right)^{2}.

$$\left(\frac{1}{8}\right)^{2}\left(x^{6}\right)^{2}\left(y^{9}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\left(\frac{1}{8}\right)^{2}x^{12}\left(y^{9}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 9 and 2 to get 18.

$$\left(\frac{1}{8}\right)^{2}x^{12}y^{18}$$

Calculate \frac{1}{8} to the power of 2 and get \frac{1}{64}.

$$\frac{1}{64}x^{12}y^{18}$$

Expand

$$\frac{x^{12}y^{18}}{64}$$

Solution Steps

Expand \left(\frac{1}{2}x^{2}y^{3}\right)^{3}.

$$\left(\left(\frac{1}{2}\right)^{3}\left(x^{2}\right)^{3}\left(y^{3}\right)^{3}\right)^{2}$$

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

$$\left(\left(\frac{1}{2}\right)^{3}x^{6}\left(y^{3}\right)^{3}\right)^{2}$$

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

$$\left(\left(\frac{1}{2}\right)^{3}x^{6}y^{9}\right)^{2}$$

Calculate \frac{1}{2} to the power of 3 and get \frac{1}{8}.

$$\left(\frac{1}{8}x^{6}y^{9}\right)^{2}$$

Expand \left(\frac{1}{8}x^{6}y^{9}\right)^{2}.

$$\left(\frac{1}{8}\right)^{2}\left(x^{6}\right)^{2}\left(y^{9}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 6 and 2 to get 12.

$$\left(\frac{1}{8}\right)^{2}x^{12}\left(y^{9}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 9 and 2 to get 18.

$$\left(\frac{1}{8}\right)^{2}x^{12}y^{18}$$

Calculate \frac{1}{8} to the power of 2 and get \frac{1}{64}.

$$\frac{1}{64}x^{12}y^{18}$$