Solve 12^4*4^3*4/6^3*8^2*27

$$\frac { 12 ^ { 4 } \times 4 ^ { 3 } \times 4 } { 6 ^ { 3 } \times 8 ^ { 2 } \times 27 }$$

Evaluate

$$\frac{128}{9}\approx 14.222222222$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 1 to get 4.

$$\frac{12^{4}\times 4^{4}}{6^{3}\times 8^{2}\times 27}$$

Calculate 12 to the power of 4 and get 20736.

$$\frac{20736\times 4^{4}}{6^{3}\times 8^{2}\times 27}$$

Calculate 4 to the power of 4 and get 256.

$$\frac{20736\times 256}{6^{3}\times 8^{2}\times 27}$$

Multiply 20736 and 256 to get 5308416.

$$\frac{5308416}{6^{3}\times 8^{2}\times 27}$$

Calculate 6 to the power of 3 and get 216.

$$\frac{5308416}{216\times 8^{2}\times 27}$$

Calculate 8 to the power of 2 and get 64.

$$\frac{5308416}{216\times 64\times 27}$$

Multiply 216 and 64 to get 13824.

$$\frac{5308416}{13824\times 27}$$

Multiply 13824 and 27 to get 373248.

$$\frac{5308416}{373248}$$

Reduce the fraction \frac{5308416}{373248} to lowest terms by extracting and canceling out 41472.

$$\frac{128}{9}$$

Factor

$$\frac{2 ^ {7}}{3 ^ {2}} = 14\frac{2}{9} = 14.222222222222221$$