(10/3) x (1/2) cubed x (1/2) to the 7th power=

Question

I know the order of operations is parenthesis, exponents, multiplication, division, addition and subtraction, but I am not sure I am doing what is correct.  The answer I have .117 or 15/128....what is the correct order to this problem?  Do I multiply 10/3 times 1/2 = 10/6 or 5/3 cubed.  .185185.  then multiply that  1/2 to seventh power which I believe is  .0071813 Can you give help me with the missing step?

Answer 1

Do your exponents first, like you said in the order of operations

 

• (10/3)*[(1/2)³]*[(1/2)⁷]
• (10/3)*(1/8)*(1/128)
• 10/3072
• 5/1536
• = .003255 (rounded)

 

Your mistake is cubing too much stuff.  The cube part is ONLY with the 1/2, and the raised to the 7th is ONLY with that second 1/2.  Note:  You could combine those 1/2 pieces together as (1/2)¹⁰ and then multiply that by your 10/3 as well.