-2.5*27^3+135*27^2-2251*27+12141

asked by guest
on Oct 17, 2024 at 11:13 pm



You asked:

Evaluate the expression: \(-2.5 \cdot {27}^{3} + 135 \cdot {27}^{2} - 2251 \cdot 27 + 12141\)

MathBot Answer:

\[-2.5 \cdot {27}^{3} + 135 \cdot {27}^{2} - 2251 \cdot 27 + 12141 = \frac{1143}{2} = 571.5\]

\[\begin{aligned}-2.5 \cdot {27}^{3} + 135 \cdot {27}^{2} - 2251 \cdot 27 + 12141& = - \cdot \left(2 + \frac{5}{10}\right) \cdot 27^{3} + 135 \cdot 27^{2} - 2251 \cdot 27 + 12141\\& = - \cdot \left(2 + \frac{1}{2}\right) \cdot 27^{3} + 135 \cdot 27^{2} - 2251 \cdot 27 + 12141\\& = - \cdot \frac{5}{2} \cdot 27^{3} + 135 \cdot 27^{2} - 2251 \cdot 27 + 12141\\& = - \cdot \frac{5}{2} \cdot 19683 + 135 \cdot 27^{2} - 2251 \cdot 27 + 12141\\& = - \frac{5}{2} \cdot 19683 + 135 \cdot 27^{2} - 2251 \cdot 27 + 12141\\& = - \frac{98415}{2} + 135 \cdot 27^{2} - 2251 \cdot 27 + 12141\\& = - \frac{98415}{2} + 135 \cdot 729 - 2251 \cdot 27 + 12141\\& = - \frac{98415}{2} + 98415 - 2251 \cdot 27 + 12141\\& = - \frac{98415}{2} + 98415 - 60777 + 12141\\& = \frac{98415}{2} - 60777 + 12141\\& = - \frac{23139}{2} + 12141\\& = \frac{1143}{2}\end{aligned}\]

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