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Evaluate the expression.
Do not round your answer.

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

Evaluate the expression.\newlineDo not round your answer.\newline12(45)23= \frac{1}{2}(4 \cdot 5)-2^{3}=

Full solution

Q. Evaluate the expression.\newlineDo not round your answer.\newline12(45)23= \frac{1}{2}(4 \cdot 5)-2^{3}=
  1. Identify Components: Identify the components of the expression.\newlineThe expression consists of a fraction (1)/(2)(4×5)(1)/(2)(4\times5) and a subtraction of 22 raised to the power of 33, which is 232^{3}.
  2. Calculate Fraction: Calculate the value of the fraction (1)/(2)(45)(1)/(2)(4*5).\newlineFirst, calculate the denominator: 2×4×5=8×5=402 \times 4 \times 5 = 8 \times 5 = 40.\newlineNow, divide the numerator by the denominator: 1/401 / 40.
  3. Calculate Exponent: Calculate the value of 22 raised to the power of 33, which is 232^{3}. 232^{3} means 22 is multiplied by itself 33 times: 2×2×2=4×2=82 \times 2 \times 2 = 4 \times 2 = 8.
  4. Subtract Values: Subtract the value of 232^{3} from the fraction (1)/(2)(45)(1)/(2)(4*5). Now we have 1/4081/40 - 8. Since 88 is not a fraction, we can write it as 8/18/1 to perform the subtraction.
  5. Find Common Denominator: Find a common denominator to subtract the fractions.\newlineThe common denominator for 140\frac{1}{40} and 81\frac{8}{1} is 4040.\newlineWe need to convert 81\frac{8}{1} to a fraction with a denominator of 4040, which is 8×401×40=32040\frac{8 \times 40}{1 \times 40} = \frac{320}{40}.
  6. Perform Subtraction: Perform the subtraction of the two fractions.\newlineNow we have 14032040\frac{1}{40} - \frac{320}{40}.\newlineSubtract the numerators: 1320=3191 - 320 = -319.\newlineThe result is 31940\frac{-319}{40}.
  7. Simplify Result: Simplify the result, if possible.\newlineThe fraction 31940-\frac{319}{40} is already in its simplest form, so no further simplification is needed.