Solve (-2/3)^{-2}*(+2/3)^4+[(+1/2)^2]^3:2^-4

$$( \frac { - 2 } { 3 } ) ^ { - 2 } \cdot ( \frac { + 2 } { 3 } ) ^ { 4 } + [ ( + \frac { 1 } { 2 } ) ^ { 2 } ] ^ { 3 } : 2 ^ { - 4 }$$

Evaluate

$$\frac{25}{36}\approx 0.694444444$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\left(\frac{-2}{3}\right)^{-2}\times \left(\frac{2}{3}\right)^{4}+\frac{\left(\frac{1}{2}\right)^{6}}{2^{-4}}$$

Fraction \frac{-2}{3} can be rewritten as -\frac{2}{3} by extracting the negative sign.

$$\left(-\frac{2}{3}\right)^{-2}\times \left(\frac{2}{3}\right)^{4}+\frac{\left(\frac{1}{2}\right)^{6}}{2^{-4}}$$

Calculate -\frac{2}{3} to the power of -2 and get \frac{9}{4}.

$$\frac{9}{4}\times \left(\frac{2}{3}\right)^{4}+\frac{\left(\frac{1}{2}\right)^{6}}{2^{-4}}$$

Calculate \frac{2}{3} to the power of 4 and get \frac{16}{81}.

$$\frac{9}{4}\times \frac{16}{81}+\frac{\left(\frac{1}{2}\right)^{6}}{2^{-4}}$$

Multiply \frac{9}{4} and \frac{16}{81} to get \frac{4}{9}.

$$\frac{4}{9}+\frac{\left(\frac{1}{2}\right)^{6}}{2^{-4}}$$

Calculate \frac{1}{2} to the power of 6 and get \frac{1}{64}.

$$\frac{4}{9}+\frac{\frac{1}{64}}{2^{-4}}$$

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

$$\frac{4}{9}+\frac{\frac{1}{64}}{\frac{1}{16}}$$

Divide \frac{1}{64} by \frac{1}{16} by multiplying \frac{1}{64} by the reciprocal of \frac{1}{16}.

$$\frac{4}{9}+\frac{1}{64}\times 16$$

Multiply \frac{1}{64} and 16 to get \frac{1}{4}.

$$\frac{4}{9}+\frac{1}{4}$$

Add \frac{4}{9} and \frac{1}{4} to get \frac{25}{36}.

$$\frac{25}{36}$$

Factor

$$\frac{5 ^ {2}}{2 ^ {2} \cdot 3 ^ {2}} = 0.6944444444444444$$