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Evaluate the expression 2^(x)-x^(2) for x=5.

Evaluate the expression 2x−x2 2^{x}-x^{2} for x=5 x=5 .

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Full solution

Q. Evaluate the expression 2x−x2 2^{x}-x^{2} for x=5 x=5 .
  1. Substitute xx in expression: Substitute the value of xx into the expression.\newlineWe are given the expression 2x−x22^{x} - x^{2} and we need to evaluate it for x=5x=5.\newlineLet's substitute xx with 55 in the expression.\newline25−522^{5} - 5^{2}
  2. Calculate first term: Calculate the first term of the expression.\newlineWe need to calculate 22 raised to the power of 55.\newline25=2×2×2×2×2=322^{5} = 2 \times 2 \times 2 \times 2 \times 2 = 32
  3. Calculate second term: Calculate the second term of the expression.\newlineNow we need to calculate 55 squared.\newline52=5×5=255^{2} = 5 \times 5 = 25
  4. Subtract terms: Subtract the second term from the first term.\newlineNow we subtract the value of 525^2 from 22 raised to the power of 55.\newline32−25=732 - 25 = 7

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