Q. Evaluate the expression.Do not round your answer.21(4⋅5)−23=
Identify Components: Identify the components of the expression.The expression consists of a fraction(1)/(2)(4×5) and a subtraction of 2 raised to the power of 3, which is 23.
Calculate Fraction: Calculate the value of the fraction (1)/(2)(4∗5).First, calculate the denominator: 2×4×5=8×5=40.Now, divide the numerator by the denominator: 1/40.
Calculate Exponent: Calculate the value of 2 raised to the power of 3, which is 23. 23 means 2 is multiplied by itself 3 times: 2×2×2=4×2=8.
Subtract Values: Subtract the value of 23 from the fraction (1)/(2)(4∗5). Now we have 1/40−8. Since 8 is not a fraction, we can write it as 8/1 to perform the subtraction.
Find Common Denominator: Find a common denominator to subtract the fractions.The common denominator for 401 and 18 is 40.We need to convert 18 to a fraction with a denominator of 40, which is 1×408×40=40320.
Perform Subtraction: Perform the subtraction of the two fractions.Now we have 401−40320.Subtract the numerators: 1−320=−319.The result is 40−319.
Simplify Result: Simplify the result, if possible.The fraction −40319 is already in its simplest form, so no further simplification is needed.