Solve 2left(1-1/2right)+left(2^2right)^-3/-frac{3{4}--3+2/53/8}=frac{325}{768}=423*2

$$\frac{ 2 \left( 1- \frac{ 1 }{ 2 } \right) + { \left( { 2 }^{ 2 } \right) }^{ -3 } }{ - \frac{ 3 }{ 4 } --3+ \frac{ 2 }{ 5 } \frac{ 3 }{ 8 } } = \frac{ 325 }{ 768 } = 423 \cdot 2$$

Verify

Solution Steps

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

$$\frac{2\left(1-\frac{1}{2}\right)+2^{-6}}{-\frac{3}{4}-\left(-3\right)+\frac{2}{5}\times \frac{3}{8}}=\frac{325}{768}\text{ and }\frac{325}{768}=423\times 2$$

Subtract \frac{1}{2} from 1 to get \frac{1}{2}.

$$\frac{2\times \frac{1}{2}+2^{-6}}{-\frac{3}{4}-\left(-3\right)+\frac{2}{5}\times \frac{3}{8}}=\frac{325}{768}\text{ and }\frac{325}{768}=423\times 2$$

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

$$\frac{1+2^{-6}}{-\frac{3}{4}-\left(-3\right)+\frac{2}{5}\times \frac{3}{8}}=\frac{325}{768}\text{ and }\frac{325}{768}=423\times 2$$

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

$$\frac{1+\frac{1}{64}}{-\frac{3}{4}-\left(-3\right)+\frac{2}{5}\times \frac{3}{8}}=\frac{325}{768}\text{ and }\frac{325}{768}=423\times 2$$

Add 1 and \frac{1}{64} to get \frac{65}{64}.

$$\frac{\frac{65}{64}}{-\frac{3}{4}-\left(-3\right)+\frac{2}{5}\times \frac{3}{8}}=\frac{325}{768}\text{ and }\frac{325}{768}=423\times 2$$

The opposite of -3 is 3.

$$\frac{\frac{65}{64}}{-\frac{3}{4}+3+\frac{2}{5}\times \frac{3}{8}}=\frac{325}{768}\text{ and }\frac{325}{768}=423\times 2$$

Add -\frac{3}{4} and 3 to get \frac{9}{4}.

$$\frac{\frac{65}{64}}{\frac{9}{4}+\frac{2}{5}\times \frac{3}{8}}=\frac{325}{768}\text{ and }\frac{325}{768}=423\times 2$$

Multiply \frac{2}{5} and \frac{3}{8} to get \frac{3}{20}.

$$\frac{\frac{65}{64}}{\frac{9}{4}+\frac{3}{20}}=\frac{325}{768}\text{ and }\frac{325}{768}=423\times 2$$

Add \frac{9}{4} and \frac{3}{20} to get \frac{12}{5}.

$$\frac{\frac{65}{64}}{\frac{12}{5}}=\frac{325}{768}\text{ and }\frac{325}{768}=423\times 2$$

Divide \frac{65}{64} by \frac{12}{5} by multiplying \frac{65}{64} by the reciprocal of \frac{12}{5}.

$$\frac{65}{64}\times \frac{5}{12}=\frac{325}{768}\text{ and }\frac{325}{768}=423\times 2$$

Multiply \frac{65}{64} and \frac{5}{12} to get \frac{325}{768}.

$$\frac{325}{768}=\frac{325}{768}\text{ and }\frac{325}{768}=423\times 2$$

Compare \frac{325}{768} and \frac{325}{768}.

$$\text{true}\text{ and }\frac{325}{768}=423\times 2$$

Multiply 423 and 2 to get 846.

$$\text{true}\text{ and }\frac{325}{768}=846$$

Convert 846 to fraction \frac{649728}{768}.

$$\text{true}\text{ and }\frac{325}{768}=\frac{649728}{768}$$

Compare \frac{325}{768} and \frac{649728}{768}.

$$\text{true}\text{ and }\text{false}$$

The conjunction of \text{true} and \text{false} is \text{false}.

$$\text{false}$$