ANSWER
6a
EXPLANATION
[tex]\frac{a}{2^3}(64)-12a\div6[/tex]The order of operations is always the same:
0. Parenthesis
,1. Exponents (include powers and roots)
,2. Multiplications and divisions
,3. Additions and subtractions
Let's take a look at the given expression. We have two terms - which are separated by a minus sign. In the first term there's a parenthesis so we have to solve what's inside first. Note that what's inside the parenthesis is just a number, no operation to be done. Therefore for the first step we have:
[tex]\frac{a}{2^3}\times64-12a\div6[/tex]Now, again in the first term there's an exponent in the denominator. We have no exponents in the second term. Solving 2³ = 8:
[tex]\frac{a}{8^{}}\times64-12a\div6[/tex]The third operations to solve are multiplications and divisions. We have many of those, but since we have a variable a, it is convenient if we solve the division first in the first term:
[tex]a\times\frac{64}{8}=a\times8[/tex]And the division of the second term:
[tex]12a\div6=(12\div6)a=2a[/tex]Therefore after solving the third operations we have:
[tex]8a-2a[/tex]Now we do the subtraction. As mentioned before, there's a variable involved so to solve the subtraction we have to combine like terms. In this case, both terms contain the variable so we take it as common factor:
[tex]a(8-2)[/tex]And solve the operation inside the parenthesis:
[tex]a\cdot(6)=6a[/tex]Hence, the expression simplifies to 6a
