Solve (18^2)^-2*81/6^3+108*24^-4

$$\frac { ( 18 ^ { 2 } ) ^ { - 2 } \cdot 81 } { 6 ^ { 3 } + 108 \cdot 24 ^ { - 4 } }$$

Evaluate

$$\frac{64}{17915931}\approx 0.000003572$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and -2 to get -4.

$$\frac{18^{-4}\times 81}{6^{3}+108\times 24^{-4}}$$

Calculate 18 to the power of -4 and get \frac{1}{104976}.

$$\frac{\frac{1}{104976}\times 81}{6^{3}+108\times 24^{-4}}$$

Multiply \frac{1}{104976} and 81 to get \frac{1}{1296}.

$$\frac{\frac{1}{1296}}{6^{3}+108\times 24^{-4}}$$

Calculate 6 to the power of 3 and get 216.

$$\frac{\frac{1}{1296}}{216+108\times 24^{-4}}$$

Calculate 24 to the power of -4 and get \frac{1}{331776}.

$$\frac{\frac{1}{1296}}{216+108\times \frac{1}{331776}}$$

Multiply 108 and \frac{1}{331776} to get \frac{1}{3072}.

$$\frac{\frac{1}{1296}}{216+\frac{1}{3072}}$$

Add 216 and \frac{1}{3072} to get \frac{663553}{3072}.

$$\frac{\frac{1}{1296}}{\frac{663553}{3072}}$$

Divide \frac{1}{1296} by \frac{663553}{3072} by multiplying \frac{1}{1296} by the reciprocal of \frac{663553}{3072}.

$$\frac{1}{1296}\times \frac{3072}{663553}$$

Multiply \frac{1}{1296} and \frac{3072}{663553} to get \frac{64}{17915931}.

$$\frac{64}{17915931}$$

Factor

$$\frac{2 ^ {6}}{3 ^ {3} \cdot 11 \cdot 179 \cdot 337} = 3.5722397010794475 \times 10^{-6}$$