Solve (4^-2-3^2-5^3)^-1

$$( 4 ^ { - 2 } - 3 ^ { 2 } - 5 ^ { 3 } ) ^ { - 1 }$$

Evaluate

$$-\frac{16}{2143}\approx -0.007466169$$

Solution Steps

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

$$\left(\frac{1}{16}-3^{2}-5^{3}\right)^{-1}$$

Calculate 3 to the power of 2 and get 9.

$$\left(\frac{1}{16}-9-5^{3}\right)^{-1}$$

Subtract 9 from \frac{1}{16} to get -\frac{143}{16}.

$$\left(-\frac{143}{16}-5^{3}\right)^{-1}$$

Calculate 5 to the power of 3 and get 125.

$$\left(-\frac{143}{16}-125\right)^{-1}$$

Subtract 125 from -\frac{143}{16} to get -\frac{2143}{16}.

$$\left(-\frac{2143}{16}\right)^{-1}$$

Calculate -\frac{2143}{16} to the power of -1 and get -\frac{16}{2143}.

$$-\frac{16}{2143}$$

Factor

$$-\frac{16}{2143} = -0.007466168922071862$$