Solve (11/3)^5*(11/2)^5=?

$$( 1 \frac { 1 } { 3 } ) ^ { 5 } \cdot ( 1 \frac { 1 } { 2 } ) ^ { 5 } = ?$$

Evaluate

$$32$$

Solution Steps

Multiply 1 and 3 to get 3.

$$\left(\frac{3+1}{3}\right)^{5}\times \left(\frac{1\times 2+1}{2}\right)^{5}$$

Add 3 and 1 to get 4.

$$\left(\frac{4}{3}\right)^{5}\times \left(\frac{1\times 2+1}{2}\right)^{5}$$

Calculate \frac{4}{3} to the power of 5 and get \frac{1024}{243}.

$$\frac{1024}{243}\times \left(\frac{1\times 2+1}{2}\right)^{5}$$

Multiply 1 and 2 to get 2.

$$\frac{1024}{243}\times \left(\frac{2+1}{2}\right)^{5}$$

Add 2 and 1 to get 3.

$$\frac{1024}{243}\times \left(\frac{3}{2}\right)^{5}$$

Calculate \frac{3}{2} to the power of 5 and get \frac{243}{32}.

$$\frac{1024}{243}\times \frac{243}{32}$$

Multiply \frac{1024}{243} and \frac{243}{32} to get 32.

$$32$$

Factor

$$2^{5}$$