Solve 2^33*(2^-131/3)3/2^73^4

$$\frac{ { 2 }^{ 3 } 3 \times ( { 2 }^{ -1 } 3 \frac{ 1 }{ 3 } )3 }{ { 2 }^{ 7 } { 3 }^{ 4 } }$$

Evaluate

$$\frac{5}{432}\approx 0.011574074$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and -1 to get 2.

$$\frac{2^{2}\times 3\times \frac{3\times 3+1}{3}\times 3}{2^{7}\times 3^{4}}$$

Calculate 2 to the power of 2 and get 4.

$$\frac{4\times 3\times \frac{3\times 3+1}{3}\times 3}{2^{7}\times 3^{4}}$$

Multiply 4 and 3 to get 12.

$$\frac{12\times \frac{3\times 3+1}{3}\times 3}{2^{7}\times 3^{4}}$$

Multiply 3 and 3 to get 9.

$$\frac{12\times \frac{9+1}{3}\times 3}{2^{7}\times 3^{4}}$$

Add 9 and 1 to get 10.

$$\frac{12\times \frac{10}{3}\times 3}{2^{7}\times 3^{4}}$$

Multiply 12 and \frac{10}{3} to get 40.

$$\frac{40\times 3}{2^{7}\times 3^{4}}$$

Multiply 40 and 3 to get 120.

$$\frac{120}{2^{7}\times 3^{4}}$$

Calculate 2 to the power of 7 and get 128.

$$\frac{120}{128\times 3^{4}}$$

Calculate 3 to the power of 4 and get 81.

$$\frac{120}{128\times 81}$$

Multiply 128 and 81 to get 10368.

$$\frac{120}{10368}$$

Reduce the fraction \frac{120}{10368} to lowest terms by extracting and canceling out 24.

$$\frac{5}{432}$$

Factor

$$\frac{5}{2 ^ {4} \cdot 3 ^ {3}} = 0.011574074074074073$$