Solve (1/4)^x+4/5+2/5:(2/3)^3

$$( \frac { 1 } { 4 } ) ^ { x } + \frac { 4 } { 5 } + \frac { 2 } { 5 } : ( \frac { 2 } { 3 } ) ^ { 3 }$$

Factor

$$\frac{\frac{20}{\left(2^{x}\right)^{2}}+43}{20}$$

Solution Steps

Calculate \frac{2}{3} to the power of 3 and get \frac{8}{27}.

$$factor(\left(\frac{1}{4}\right)^{x}+\frac{4}{5}+\frac{\frac{2}{5}}{\frac{8}{27}})$$

Divide \frac{2}{5} by \frac{8}{27} by multiplying \frac{2}{5} by the reciprocal of \frac{8}{27}.

$$factor(\left(\frac{1}{4}\right)^{x}+\frac{4}{5}+\frac{2}{5}\times \frac{27}{8})$$

Multiply \frac{2}{5} and \frac{27}{8} to get \frac{27}{20}.

$$factor(\left(\frac{1}{4}\right)^{x}+\frac{4}{5}+\frac{27}{20})$$

Add \frac{4}{5} and \frac{27}{20} to get \frac{43}{20}.

$$factor(\left(\frac{1}{4}\right)^{x}+\frac{43}{20})$$

Factor out \frac{1}{20}.

$$\frac{20\times \left(\frac{1}{4}\right)^{x}+43}{20}$$

Evaluate

$$\frac{1}{2^{2x}}+\frac{43}{20}$$