Solve frac{9-16*27*3^{-2}}{2^6*3^-2*3^3*2^6}

$$\frac { 9 - 16 \cdot 27 \cdot 3 ^ { - 2 } } { 2 ^ { 6 } \cdot 3 ^ { - 2 } \cdot 3 ^ { 3 } \cdot 2 ^ { 6 } }$$

Evaluate

$$-\frac{13}{4096}\approx -0.003173828$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 6 to get 12.

$$\frac{9-16\times 27\times 3^{-2}}{2^{12}\times 3^{-2}\times 3^{3}}$$

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

$$\frac{9-16\times 27\times 3^{-2}}{2^{12}\times 3^{1}}$$

Multiply 16 and 27 to get 432.

$$\frac{9-432\times 3^{-2}}{2^{12}\times 3^{1}}$$

Calculate 3 to the power of -2 and get \frac{1}{9}.

$$\frac{9-432\times \frac{1}{9}}{2^{12}\times 3^{1}}$$

Multiply 432 and \frac{1}{9} to get 48.

$$\frac{9-48}{2^{12}\times 3^{1}}$$

Subtract 48 from 9 to get -39.

$$\frac{-39}{2^{12}\times 3^{1}}$$

Calculate 2 to the power of 12 and get 4096.

$$\frac{-39}{4096\times 3^{1}}$$

Calculate 3 to the power of 1 and get 3.

$$\frac{-39}{4096\times 3}$$

Multiply 4096 and 3 to get 12288.

$$\frac{-39}{12288}$$

Reduce the fraction \frac{-39}{12288} to lowest terms by extracting and canceling out 3.

$$-\frac{13}{4096}$$

Factor

$$-\frac{13}{4096} = -0.003173828125$$