Question

Simplify the expression below by following the order of operations and combining like terms. Do not put spaces between characters. \frac{a}{2^3}(64)-12a \div6 The expression simplifies to:

Answer 1

6a

Step-by-step explanation

`(a)/(2^3)(64)-12a/6`

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:

`(a)/(2^3)*64-12a/6`

Now, again in the first term there's an exponent in the denominator. We have no exponents in the second term. Solving 2³ = 8:

`\frac{a}{8^{}}*64-12a/6`

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:

`a*(64)/(8)=a*8`

And the division of the second term:

`12a/6=(12/6)a=2a`

Therefore after solving the third operations we have:

`8a-2a`

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:

`a(8-2)`

And solve the operation inside the parenthesis:

`a\cdot(6)=6a`

Hence, the expression simplifies to 6a