Solve 2^-44^239^-13^-2/{2^-58{3}^-39}

$$\frac{ { 2 }^{ -4 } { 4 }^{ 2 } 3 { 9 }^{ -1 } { 3 }^{ -2 } }{ { 2 }^{ -5 } 8 { 3 }^{ -3 } 9 }$$

Evaluate

$$\frac{4}{9}\approx 0.444444444$$

Solution Steps

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

$$\frac{2^{-4}\times 4^{2}\times 3^{-1}\times 9^{-1}}{2^{-5}\times 8\times 3^{-3}\times 9}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{2^{1}\times 3^{2}\times 4^{2}\times \frac{1}{9}}{8\times 9}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{2^{1}\times 3^{2}\times 4^{2}}{8\times 9^{2}}$$

Calculate 2 to the power of 1 and get 2.

$$\frac{2\times 3^{2}\times 4^{2}}{8\times 9^{2}}$$

Calculate 3 to the power of 2 and get 9.

$$\frac{2\times 9\times 4^{2}}{8\times 9^{2}}$$

Multiply 2 and 9 to get 18.

$$\frac{18\times 4^{2}}{8\times 9^{2}}$$

Calculate 4 to the power of 2 and get 16.

$$\frac{18\times 16}{8\times 9^{2}}$$

Multiply 18 and 16 to get 288.

$$\frac{288}{8\times 9^{2}}$$

Calculate 9 to the power of 2 and get 81.

$$\frac{288}{8\times 81}$$

Multiply 8 and 81 to get 648.

$$\frac{288}{648}$$

Reduce the fraction \frac{288}{648} to lowest terms by extracting and canceling out 72.

$$\frac{4}{9}$$

Factor

$$\frac{2 ^ {2}}{3 ^ {2}} = 0.4444444444444444$$