Solve frac{-2^-3/{left(-frac{1{2}right)}^-2}-9^0}{-9^-2}

$$\frac{ \frac{ { -2 }^{ -3 } }{ { \left(- \frac{ 1 }{ 2 } \right) }^{ -2 } } { -9 }^{ 0 } }{ { -9 }^{ -2 } }$$

Evaluate

$$-\frac{81}{32}=-2.53125$$

Solution Steps

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

$$\frac{\frac{-\frac{1}{8}}{\left(-\frac{1}{2}\right)^{-2}}\left(-9\right)^{0}}{\left(-9\right)^{-2}}$$

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

$$\frac{\frac{-\frac{1}{8}}{4}\left(-9\right)^{0}}{\left(-9\right)^{-2}}$$

Express \frac{-\frac{1}{8}}{4} as a single fraction.

$$\frac{\frac{-1}{8\times 4}\left(-9\right)^{0}}{\left(-9\right)^{-2}}$$

Multiply 8 and 4 to get 32.

$$\frac{\frac{-1}{32}\left(-9\right)^{0}}{\left(-9\right)^{-2}}$$

Fraction \frac{-1}{32} can be rewritten as -\frac{1}{32} by extracting the negative sign.

$$\frac{-\frac{1}{32}\left(-9\right)^{0}}{\left(-9\right)^{-2}}$$

Calculate -9 to the power of 0 and get 1.

$$\frac{-\frac{1}{32}}{\left(-9\right)^{-2}}$$

Calculate -9 to the power of -2 and get \frac{1}{81}.

$$\frac{-\frac{1}{32}}{\frac{1}{81}}$$

Divide -\frac{1}{32} by \frac{1}{81} by multiplying -\frac{1}{32} by the reciprocal of \frac{1}{81}.

$$-\frac{1}{32}\times 81$$

Multiply -\frac{1}{32} and 81 to get -\frac{81}{32}.

$$-\frac{81}{32}$$

Factor

$$-\frac{81}{32} = -2\frac{17}{32} = -2.53125$$