Solve (2(1-1/2)+[(2)^2]^-3/-frac{3{4}-(-3)+2/5*3/8})=frac{325}{768}=0.4232

$$( \frac { 2 ( 1 - \frac { 1 } { 2 } ) + [ ( 2 ) ^ { 2 } ] ^ { - 3 } } { - \frac { 3 } { 4 } - ( - 3 ) + \frac { 2 } { 5 } \cdot \frac { 3 } { 8 } } ) = \frac { 325 } { 768 } = 0.4232$$

Verify

Solution Steps

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

$$\frac{2\left(1-\frac{1}{2}\right)+2^{-6}}{-\frac{3}{4}-\left(-3\right)+\frac{2}{5}\times \frac{3}{8}}=\frac{325}{768}\text{ and }\frac{325}{768}=0.4232$$

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

$$\frac{2\times \frac{1}{2}+2^{-6}}{-\frac{3}{4}-\left(-3\right)+\frac{2}{5}\times \frac{3}{8}}=\frac{325}{768}\text{ and }\frac{325}{768}=0.4232$$

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

$$\frac{1+2^{-6}}{-\frac{3}{4}-\left(-3\right)+\frac{2}{5}\times \frac{3}{8}}=\frac{325}{768}\text{ and }\frac{325}{768}=0.4232$$

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

$$\frac{1+\frac{1}{64}}{-\frac{3}{4}-\left(-3\right)+\frac{2}{5}\times \frac{3}{8}}=\frac{325}{768}\text{ and }\frac{325}{768}=0.4232$$

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

$$\frac{\frac{65}{64}}{-\frac{3}{4}-\left(-3\right)+\frac{2}{5}\times \frac{3}{8}}=\frac{325}{768}\text{ and }\frac{325}{768}=0.4232$$

The opposite of -3 is 3.

$$\frac{\frac{65}{64}}{-\frac{3}{4}+3+\frac{2}{5}\times \frac{3}{8}}=\frac{325}{768}\text{ and }\frac{325}{768}=0.4232$$

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

$$\frac{\frac{65}{64}}{\frac{9}{4}+\frac{2}{5}\times \frac{3}{8}}=\frac{325}{768}\text{ and }\frac{325}{768}=0.4232$$

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

$$\frac{\frac{65}{64}}{\frac{9}{4}+\frac{3}{20}}=\frac{325}{768}\text{ and }\frac{325}{768}=0.4232$$

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

$$\frac{\frac{65}{64}}{\frac{12}{5}}=\frac{325}{768}\text{ and }\frac{325}{768}=0.4232$$

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

$$\frac{65}{64}\times \frac{5}{12}=\frac{325}{768}\text{ and }\frac{325}{768}=0.4232$$

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

$$\frac{325}{768}=\frac{325}{768}\text{ and }\frac{325}{768}=0.4232$$

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

$$\text{true}\text{ and }\frac{325}{768}=0.4232$$

Convert decimal number 0.4232 to fraction \frac{4232}{10000}. Reduce the fraction \frac{4232}{10000} to lowest terms by extracting and canceling out 8.

$$\text{true}\text{ and }\frac{325}{768}=\frac{529}{1250}$$

Least common multiple of 768 and 1250 is 480000. Convert \frac{325}{768} and \frac{529}{1250} to fractions with denominator 480000.

$$\text{true}\text{ and }\frac{203125}{480000}=\frac{203136}{480000}$$

Compare \frac{203125}{480000} and \frac{203136}{480000}.

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

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

$$\text{false}$$