Question - Arithmetic Calculation and Evaluation
Solution:
To solve the expression given in the image, follow the order of operations, PEMDAS (Parentheses, Exponents, Multiplication and Division from left to right, Addition and Subtraction from left to right):Given expression:7 + 3 × 2^4 ÷ 8 - (9 ÷ 6 - 3)^2Let's simplify the expression step by step:1. Solve the exponentiation (2^4):7 + 3 × 16 ÷ 8 - (9 ÷ 6 - 3)^22. Perform the division inside the parentheses (9 ÷ 6):7 + 3 × 16 ÷ 8 - (1.5 - 3)^23. Solve the subtraction inside the parentheses (1.5 - 3):7 + 3 × 16 ÷ 8 - (-1.5)^24. Solve the exponentiation (-1.5)^2 (square of -1.5):7 + 3 × 16 ÷ 8 - 2.255. Perform the multiplication (3 × 16) and the division by 8:7 + 48 ÷ 8 - 2.256. Perform the division (48 ÷ 8):7 + 6 - 2.257. Add 7 and 6:13 - 2.258. Subtract 2.25 from 13:13 - 2.25 = 10.75However, none of the answer choices match this calculation. It seems we have faced an arithmetic mistake. Let us go through the calculation again more carefully.1. Solve the exponent (2^4 = 16):7 + 3 × 16 ÷ 8 - (9 ÷ 6 - 3)^22. Carry out the division (16 ÷ 8 = 2):7 + 3 × 2 - (9 ÷ 6 - 3)^23. Perform any multiplications (3 × 2 = 6):7 + 6 - (9 ÷ 6 - 3)^24. Solve the division inside the parentheses (9 ÷ 6 = 1.5):7 + 6 - (1.5 - 3)^25. Perform the subtraction inside the parentheses (1.5 - 3 = -1.5):7 + 6 - (-1.5)^26. Compute the square (-1.5 × -1.5 = 2.25):7 + 6 - 2.257. Add the 7 and 6:13 - 2.258. Finally, subtract 2.25 from 13:13 - 2.25 = 10.75After following each step carefully, the result is indeed 10.75, which does not appear to be one of the options provided. There may be a mistake in the answer choices or a misinterpretation of the question. If we consider the initial expression again and assume that order of division and multiplication as per the provided image:7 + (3 × 2^4 ÷ 8) - (9 ÷ 6 - 3)^2We may consider performing the division in the term (3 × 2^4 ÷ 8) following the left-to-right rule. In that case, we divide first and then multiply:1. Solve the exponent (2^4 = 16):7 + (3 × 16 ÷ 8) - (9 ÷ 6 - 3)^22. Perform the division first according to the left-to-right rule of division and multiplication (16 ÷ 8 = 2):7 + (3 × 2) - (9 ÷ 6 - 3)^23. Multiply (3 × 2 = 6):7 + 6 - (9 ÷ 6 - 3)^24. Solve within the parentheses for division and subtraction (9 ÷ 6 = 1.5, then 1.5 - 3 = -1.5):7 + 6 - (-1.5)^25. Calculate the square of -1.5 (-1.5 × -1.5 = 2.25):7 + 6 - 2.256. Add 7 and 6:13 - 2.257. Subtract 2.25 from 13:13 - 2.25 = 10.75Once again, the result is 10.75. The question may contain a mistake, as none of the provided answer choices match the correct calculation. Could you please double-check the problem or the answer choices?
CamTutor
In regards to math, we are professionals.
Get In Touch
Email: camtutor.ai@gmail.com