Solve frac{4^{0}+2^-1}{(-3)^2+5^-3-(-2)^3}

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

Evaluate

$$\frac{375}{4252}\approx 0.088193791$$

Solution Steps

Calculate 4 to the power of 0 and get 1.

$$\frac{1+2^{-1}}{\left(-3\right)^{2}+5^{-3}-\left(-2\right)^{3}}$$

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

$$\frac{1+\frac{1}{2}}{\left(-3\right)^{2}+5^{-3}-\left(-2\right)^{3}}$$

Add 1 and \frac{1}{2} to get \frac{3}{2}.

$$\frac{\frac{3}{2}}{\left(-3\right)^{2}+5^{-3}-\left(-2\right)^{3}}$$

Calculate -3 to the power of 2 and get 9.

$$\frac{\frac{3}{2}}{9+5^{-3}-\left(-2\right)^{3}}$$

Calculate 5 to the power of -3 and get \frac{1}{125}.

$$\frac{\frac{3}{2}}{9+\frac{1}{125}-\left(-2\right)^{3}}$$

Add 9 and \frac{1}{125} to get \frac{1126}{125}.

$$\frac{\frac{3}{2}}{\frac{1126}{125}-\left(-2\right)^{3}}$$

Calculate -2 to the power of 3 and get -8.

$$\frac{\frac{3}{2}}{\frac{1126}{125}-\left(-8\right)}$$

The opposite of -8 is 8.

$$\frac{\frac{3}{2}}{\frac{1126}{125}+8}$$

Add \frac{1126}{125} and 8 to get \frac{2126}{125}.

$$\frac{\frac{3}{2}}{\frac{2126}{125}}$$

Divide \frac{3}{2} by \frac{2126}{125} by multiplying \frac{3}{2} by the reciprocal of \frac{2126}{125}.

$$\frac{3}{2}\times \frac{125}{2126}$$

Multiply \frac{3}{2} and \frac{125}{2126} to get \frac{375}{4252}.

$$\frac{375}{4252}$$

Factor

$$\frac{3 \cdot 5 ^ {3}}{2 ^ {2} \cdot 1063} = 0.08819379115710255$$