Solve [(64)^frac{2{3}}2^-2div8^0]^-1/2

$$[ ( 64 ) ^ { \frac { 2 } { 3 } } 2 ^ { - 2 } \div 8 ^ { 0 } ] ^ { - 1 / 2 }$$

Evaluate

$$\frac{1}{2}=0.5$$

Solution Steps

Calculate 64 to the power of \frac{2}{3} and get 16.

$$\left(\frac{16\times 2^{-2}}{8^{0}}\right)^{-\frac{1}{2}}$$

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

$$\left(\frac{16\times \frac{1}{4}}{8^{0}}\right)^{-\frac{1}{2}}$$

Multiply 16 and \frac{1}{4} to get 4.

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

Calculate 8 to the power of 0 and get 1.

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

Anything divided by one gives itself.

$$4^{-\frac{1}{2}}$$

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

$$\frac{1}{2}$$

Factor

$$\frac{1}{2} = 0.5$$