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1-\left(2-0.5\right)\times \frac{1}{3}\left(\left(-\frac{1}{2}\right)^{2}-\left(\frac{1}{2}\right)^{3}\right)
Calculate 1 to the power of 4 and get 1.
1-1.5\times \frac{1}{3}\left(\left(-\frac{1}{2}\right)^{2}-\left(\frac{1}{2}\right)^{3}\right)
Subtract 0.5 from 2 to get 1.5.
1-\frac{3}{2}\times \frac{1}{3}\left(\left(-\frac{1}{2}\right)^{2}-\left(\frac{1}{2}\right)^{3}\right)
Convert decimal number 1.5 to fraction \frac{15}{10}. Reduce the fraction \frac{15}{10} to lowest terms by extracting and canceling out 5.
1-\frac{3\times 1}{2\times 3}\left(\left(-\frac{1}{2}\right)^{2}-\left(\frac{1}{2}\right)^{3}\right)
Multiply \frac{3}{2} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.
1-\frac{1}{2}\left(\left(-\frac{1}{2}\right)^{2}-\left(\frac{1}{2}\right)^{3}\right)
Cancel out 3 in both numerator and denominator.
1-\frac{1}{2}\left(\frac{1}{4}-\left(\frac{1}{2}\right)^{3}\right)
Calculate -\frac{1}{2} to the power of 2 and get \frac{1}{4}.
1-\frac{1}{2}\left(\frac{1}{4}-\frac{1}{8}\right)
Calculate \frac{1}{2} to the power of 3 and get \frac{1}{8}.
1-\frac{1}{2}\left(\frac{2}{8}-\frac{1}{8}\right)
Least common multiple of 4 and 8 is 8. Convert \frac{1}{4} and \frac{1}{8} to fractions with denominator 8.
1-\frac{1}{2}\times \frac{2-1}{8}
Since \frac{2}{8} and \frac{1}{8} have the same denominator, subtract them by subtracting their numerators.
1-\frac{1}{2}\times \frac{1}{8}
Subtract 1 from 2 to get 1.
1-\frac{1\times 1}{2\times 8}
Multiply \frac{1}{2} times \frac{1}{8} by multiplying numerator times numerator and denominator times denominator.
1-\frac{1}{16}
Do the multiplications in the fraction \frac{1\times 1}{2\times 8}.
\frac{16}{16}-\frac{1}{16}
Convert 1 to fraction \frac{16}{16}.
\frac{16-1}{16}
Since \frac{16}{16} and \frac{1}{16} have the same denominator, subtract them by subtracting their numerators.
\frac{15}{16}
Subtract 1 from 16 to get 15.