Solve (6^-1+2^-3):(5^0+4^-2)

$$( 6 ^ { - 1 } + 2 ^ { - 3 } ) : ( 5 ^ { 0 } + 4 ^ { - 2 } )$$

Evaluate

$$\frac{14}{51}\approx 0.274509804$$

Solution Steps

Calculate 6 to the power of -1 and get \frac{1}{6}.

$$\frac{\frac{1}{6}+2^{-3}}{5^{0}+4^{-2}}$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$\frac{\frac{1}{6}+\frac{1}{8}}{5^{0}+4^{-2}}$$

Add \frac{1}{6} and \frac{1}{8} to get \frac{7}{24}.

$$\frac{\frac{7}{24}}{5^{0}+4^{-2}}$$

Calculate 5 to the power of 0 and get 1.

$$\frac{\frac{7}{24}}{1+4^{-2}}$$

Calculate 4 to the power of -2 and get \frac{1}{16}.

$$\frac{\frac{7}{24}}{1+\frac{1}{16}}$$

Add 1 and \frac{1}{16} to get \frac{17}{16}.

$$\frac{\frac{7}{24}}{\frac{17}{16}}$$

Divide \frac{7}{24} by \frac{17}{16} by multiplying \frac{7}{24} by the reciprocal of \frac{17}{16}.

$$\frac{7}{24}\times \frac{16}{17}$$

Multiply \frac{7}{24} and \frac{16}{17} to get \frac{14}{51}.

$$\frac{14}{51}$$

Factor

$$\frac{2 \cdot 7}{3 \cdot 17} = 0.27450980392156865$$