(-1/2)^4-3*(-1/2)^3-2*(-1/2)^2+5

asked by guest
on Oct 24, 2024 at 8:14 am



You asked:

Evaluate the expression: \({\left( \frac{-1}{2} \right)}^{4} - 3 \cdot {\left( \frac{-1}{2} \right)}^{3} - 2 \cdot {\left( \frac{-1}{2} \right)}^{2} + 5\)

MathBot Answer:

\[{\left( \frac{-1}{2} \right)}^{4} - 3 \cdot {\left( \frac{-1}{2} \right)}^{3} - 2 \cdot {\left( \frac{-1}{2} \right)}^{2} + 5 = \frac{79}{16} = 4.9375\]

\[\begin{aligned}{\left( \frac{-1}{2} \right)}^{4} - 3 \cdot {\left( \frac{-1}{2} \right)}^{3} - 2 \cdot {\left( \frac{-1}{2} \right)}^{2} + 5& = \left(- \frac{1}{2}\right)^{4} - 3 \cdot \left(- \frac{1}{2}\right)^{3} - 2 \cdot \left(- \frac{1}{2}\right)^{2} + 5\\& = \frac{1}{16} - 3 \cdot \left(- \frac{1}{2}\right)^{3} - 2 \cdot \left(- \frac{1}{2}\right)^{2} + 5\\& = \frac{1}{16} - \frac{-3}{8} - 2 \cdot \left(- \frac{1}{2}\right)^{2} + 5\\& = \frac{1}{16} - - \frac{3}{8} - 2 \cdot \left(- \frac{1}{2}\right)^{2} + 5\\& = \frac{1}{16} + \frac{3}{8} - 2 \cdot \left(- \frac{1}{2}\right)^{2} + 5\\& = \frac{1}{16} + \frac{3}{8} - \frac{2}{4} + 5\\& = \frac{1}{16} + \frac{3}{8} - \frac{1}{2} + 5\\& = \frac{7}{16} - \frac{1}{2} + 5\\& = - \frac{1}{16} + 5\\& = \frac{79}{16}\end{aligned}\]

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