Solve {left(frac{1/2right)}^-4}{1/2}left(4^-1right)^2+{left(-1/6right)}^0

$$\frac{ { \left( \frac{ 1 }{ 2 } \right) }^{ -4 } }{ \frac{ 1 }{ 2 } } { \left( { 4 }^{ -1 } \right) }^{ 2 } + { \left(- \frac{ 1 }{ 6 } \right) }^{ 0 }$$

Evaluate

$$3$$

Solution Steps

Rewrite \frac{1}{2} as \left(\frac{1}{2}\right)^{-4}\times \left(\frac{1}{2}\right)^{5}. Cancel out \left(\frac{1}{2}\right)^{-4} in both numerator and denominator.

$$\frac{1}{\left(\frac{1}{2}\right)^{5}}\times \left(4^{-1}\right)^{2}+\left(-\frac{1}{6}\right)^{0}$$

To raise a power to another power, multiply the exponents. Multiply -1 and 2 to get -2.

$$\frac{1}{\left(\frac{1}{2}\right)^{5}}\times 4^{-2}+\left(-\frac{1}{6}\right)^{0}$$

Calculate \frac{1}{2} to the power of 5 and get \frac{1}{32}.

$$\frac{1}{\frac{1}{32}}\times 4^{-2}+\left(-\frac{1}{6}\right)^{0}$$

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

$$1\times 32\times 4^{-2}+\left(-\frac{1}{6}\right)^{0}$$

Multiply 1 and 32 to get 32.

$$32\times 4^{-2}+\left(-\frac{1}{6}\right)^{0}$$

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

$$32\times \frac{1}{16}+\left(-\frac{1}{6}\right)^{0}$$

Multiply 32 and \frac{1}{16} to get 2.

$$2+\left(-\frac{1}{6}\right)^{0}$$

Calculate -\frac{1}{6} to the power of 0 and get 1.

$$2+1$$

Add 2 and 1 to get 3.

$$3$$

Factor

$$3$$