Solve 4/5left(2^-3x+4^-2right)-1/5left(2x--2^-3right)=5^-1/{2^-3}

$$\frac{ 4 }{ 5 } \left( { 2 }^{ -3 } x+ { 4 }^{ -2 } \right) - \frac{ 1 }{ 5 } \left( 2x- { -2 }^{ -3 } \right) = \frac{ { 5 }^{ -1 } }{ { 2 }^{ -3 } }$$

Solve for x

$$x = -\frac{21}{4} = -5\frac{1}{4} = -5.25$$

Steps for Solving Linear Equation

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$\frac{4}{5}\left(\frac{1}{8}x+4^{-2}\right)-\frac{1}{5}\left(2x-\left(-2\right)^{-3}\right)=\frac{5^{-1}}{2^{-3}}$$

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

$$\frac{4}{5}\left(\frac{1}{8}x+\frac{1}{16}\right)-\frac{1}{5}\left(2x-\left(-2\right)^{-3}\right)=\frac{5^{-1}}{2^{-3}}$$

Use the distributive property to multiply \frac{4}{5} by \frac{1}{8}x+\frac{1}{16}.

$$\frac{1}{10}x+\frac{1}{20}-\frac{1}{5}\left(2x-\left(-2\right)^{-3}\right)=\frac{5^{-1}}{2^{-3}}$$

Calculate -2 to the power of -3 and get -\frac{1}{8}.

$$\frac{1}{10}x+\frac{1}{20}-\frac{1}{5}\left(2x-\left(-\frac{1}{8}\right)\right)=\frac{5^{-1}}{2^{-3}}$$

The opposite of -\frac{1}{8} is \frac{1}{8}.

$$\frac{1}{10}x+\frac{1}{20}-\frac{1}{5}\left(2x+\frac{1}{8}\right)=\frac{5^{-1}}{2^{-3}}$$

Use the distributive property to multiply -\frac{1}{5} by 2x+\frac{1}{8}.

$$\frac{1}{10}x+\frac{1}{20}-\frac{2}{5}x-\frac{1}{40}=\frac{5^{-1}}{2^{-3}}$$

Combine \frac{1}{10}x and -\frac{2}{5}x to get -\frac{3}{10}x.

$$-\frac{3}{10}x+\frac{1}{20}-\frac{1}{40}=\frac{5^{-1}}{2^{-3}}$$

Subtract \frac{1}{40} from \frac{1}{20} to get \frac{1}{40}.

$$-\frac{3}{10}x+\frac{1}{40}=\frac{5^{-1}}{2^{-3}}$$

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

$$-\frac{3}{10}x+\frac{1}{40}=\frac{\frac{1}{5}}{2^{-3}}$$

Calculate 2 to the power of -3 and get \frac{1}{8}.

$$-\frac{3}{10}x+\frac{1}{40}=\frac{\frac{1}{5}}{\frac{1}{8}}$$

Divide \frac{1}{5} by \frac{1}{8} by multiplying \frac{1}{5} by the reciprocal of \frac{1}{8}.

$$-\frac{3}{10}x+\frac{1}{40}=\frac{1}{5}\times 8$$

Multiply \frac{1}{5} and 8 to get \frac{8}{5}.

$$-\frac{3}{10}x+\frac{1}{40}=\frac{8}{5}$$

Subtract \frac{1}{40} from both sides.

$$-\frac{3}{10}x=\frac{8}{5}-\frac{1}{40}$$

Subtract \frac{1}{40} from \frac{8}{5} to get \frac{63}{40}.

$$-\frac{3}{10}x=\frac{63}{40}$$

Multiply both sides by -\frac{10}{3}, the reciprocal of -\frac{3}{10}.

$$x=\frac{63}{40}\left(-\frac{10}{3}\right)$$

Multiply \frac{63}{40} and -\frac{10}{3} to get -\frac{21}{4}.

$$x=-\frac{21}{4}$$