Solve (-1/4)^2div(-1/2)^4*(-1)^6-(13/8+11/3-2frac{3}{4})*48

$$( - \frac { 1 } { 4 } ) ^ { 2 } \div ( - \frac { 1 } { 2 } ) ^ { 4 } \times ( - 1 ) ^ { 6 } - ( 1 \frac { 3 } { 8 } + 1 \frac { 1 } { 3 } - 2 \frac { 3 } { 4 } ) \times 48$$

Evaluate

$$3$$

Solution Steps

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

$$\frac{\frac{1}{16}}{\left(-\frac{1}{2}\right)^{4}}\left(-1\right)^{6}-\left(\frac{1\times 8+3}{8}+\frac{1\times 3+1}{3}-\frac{2\times 4+3}{4}\right)\times 48$$

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

$$\frac{\frac{1}{16}}{\frac{1}{16}}\left(-1\right)^{6}-\left(\frac{1\times 8+3}{8}+\frac{1\times 3+1}{3}-\frac{2\times 4+3}{4}\right)\times 48$$

Divide \frac{1}{16} by \frac{1}{16} to get 1.

$$1\left(-1\right)^{6}-\left(\frac{1\times 8+3}{8}+\frac{1\times 3+1}{3}-\frac{2\times 4+3}{4}\right)\times 48$$

Calculate -1 to the power of 6 and get 1.

$$1\times 1-\left(\frac{1\times 8+3}{8}+\frac{1\times 3+1}{3}-\frac{2\times 4+3}{4}\right)\times 48$$

Multiply 1 and 1 to get 1.

$$1-\left(\frac{1\times 8+3}{8}+\frac{1\times 3+1}{3}-\frac{2\times 4+3}{4}\right)\times 48$$

Multiply 1 and 8 to get 8.

$$1-\left(\frac{8+3}{8}+\frac{1\times 3+1}{3}-\frac{2\times 4+3}{4}\right)\times 48$$

Add 8 and 3 to get 11.

$$1-\left(\frac{11}{8}+\frac{1\times 3+1}{3}-\frac{2\times 4+3}{4}\right)\times 48$$

Multiply 1 and 3 to get 3.

$$1-\left(\frac{11}{8}+\frac{3+1}{3}-\frac{2\times 4+3}{4}\right)\times 48$$

Add 3 and 1 to get 4.

$$1-\left(\frac{11}{8}+\frac{4}{3}-\frac{2\times 4+3}{4}\right)\times 48$$

Least common multiple of 8 and 3 is 24. Convert \frac{11}{8} and \frac{4}{3} to fractions with denominator 24.

$$1-\left(\frac{33}{24}+\frac{32}{24}-\frac{2\times 4+3}{4}\right)\times 48$$

Since \frac{33}{24} and \frac{32}{24} have the same denominator, add them by adding their numerators.

$$1-\left(\frac{33+32}{24}-\frac{2\times 4+3}{4}\right)\times 48$$

Add 33 and 32 to get 65.

$$1-\left(\frac{65}{24}-\frac{2\times 4+3}{4}\right)\times 48$$

Multiply 2 and 4 to get 8.

$$1-\left(\frac{65}{24}-\frac{8+3}{4}\right)\times 48$$

Add 8 and 3 to get 11.

$$1-\left(\frac{65}{24}-\frac{11}{4}\right)\times 48$$

Least common multiple of 24 and 4 is 24. Convert \frac{65}{24} and \frac{11}{4} to fractions with denominator 24.

$$1-\left(\frac{65}{24}-\frac{66}{24}\right)\times 48$$

Since \frac{65}{24} and \frac{66}{24} have the same denominator, subtract them by subtracting their numerators.

$$1-\frac{65-66}{24}\times 48$$

Subtract 66 from 65 to get -1.

$$1-\left(-\frac{1}{24}\times 48\right)$$

Express -\frac{1}{24}\times 48 as a single fraction.

$$1-\frac{-48}{24}$$

Divide -48 by 24 to get -2.

$$1-\left(-2\right)$$

The opposite of -2 is 2.

$$1+2$$

Add 1 and 2 to get 3.

$$3$$

Factor

$$3$$