Solve {left(0.5^-3/{left(frac{1{2}right)}^-50.5}right)}^-2

$${ \left( \frac{ { 0.5 }^{ -3 } }{ { \left( \frac{ 1 }{ 2 } \right) }^{ -5 } 0.5 } \right) }^{ -2 }$$

Evaluate

$$4$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -5 and 1 to get -4.

$$\left(\frac{0.5^{-3}}{\left(\frac{1}{2}\right)^{-4}}\right)^{-2}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -4 from -3 to get 1.

$$\left(0.5^{1}\right)^{-2}$$

Calculate 0.5 to the power of 1 and get 0.5.

$$0.5^{-2}$$

Calculate 0.5 to the power of -2 and get 4.

$$4$$

Factor

$$2^{2}$$