Parentheses in advanced Order of Operations: Solving the problem

According to the order of operations rules, we must first solve the expressions inside of the parentheses:

$15-9=6$

$7-3=4$

We obtain the following expression:

$6\times4=24$

According to the order of operations, we will first solve the expressions in parentheses, and then multiply:

$(12-6+9)=(6+9)=15$

$(7+3)=10$

Now let's solve the multiplication problem:

$15\times10=150$

According to the order of operations, we'll first solve the exercises in parentheses:

$(16-6)=10$

$(7-3)=4$

Now we'll get the exercise:

$10\times9+4$

We'll put the multiplication exercise in parentheses to avoid confusion in the rest of the solution:

$(10\times9)+4=$

According to the order of operations, we'll solve the multiplication exercise and then add:

$90+4=94$

According to the order of operations rules, we must first solve the expression within the parentheses:

$85+5=90$

We should obtain the following expression:

$90:10=9$

According to the order of operations, first we solve the exercise within parentheses:

$30+6=36$

Now we solve the exercise

$36:4\times3=$

Since the exercise only involves multiplication and division operations, we solve from left to right:

$36:4=9$

$9\times3=27$

According to the order of operations, we will first solve the multiplication exercises in parentheses:

$(13\times2)=26$

$(12\times1.5)=18$

Now we will subtract:

$26-18=8$

First, we perform the operation inside the parentheses:

$12:3(2)$

When there is no mathematical operation between parentheses and a number, we assume it is a multiplication.

Therefore, we can also write the exercise like this:

$12:3\times2$

Here we solve from left to right:

$12:3\times2=4\times2=8$

First, we solve the exercise in the parentheses

$(1+9:9)=$

According to the order of operations, we first divide and then add:

$1+1=2$

Now we obtain the exercise:

$20-2=18$

According to the rules of the order of operations, we first solve the exercise within parentheses:

$4+5=9$

Now we obtain the exercise:

$2\times3-9:2=$

We place in parentheses the multiplication and division exercises:

$(2\times3)-(9:2)=$

We solve the exercises within parentheses:

$2\times3=6$

$9:2=4.5$

Now we obtain the exercise:

$6-4.5=1.5$

According to the rules of the order of operations, we first solve the exercise within parentheses from left to right:

$8:4=2$

$2:2=1$

Now we get the exercise:

$1-3-1=$

We solve the exercise from left to right:

$1-3=-2$

$-2-1=-3$

First, we solve the exercise in the parentheses

$(20-4\times5)=$

According to the order of operations, we first multiply and then subtract:

$20-20=0$

Now we obtain the exercise:

$19\times0=0$

According to the order of operations in arithmetic, parentheses take precedence over everything else.

Inside the parentheses, we will first solve the multiplication problem and then add.

To make solving the multiplication problem easier, we will convert 8 to a simple fraction:

$2\times(3+\frac{1}{2}\times\frac{8}{1})=2\times(3+\frac{8}{2})=2\times(3+4)$

Now we will solve the addition problem inside the parentheses and finally multiply:

$2\times7=14$

To solve the expression $[(4-2)^2]^3$, we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

Step 1: Solve the innermost parentheses:

The expression inside the innermost parentheses is $4-2$. We perform the subtraction:

$4-2 = 2$

Step 2: Apply the exponentiation:

Next, we take the result of the subtraction and apply the squaring operation $((2)^2)$:

$2^2 = 4$

Step 3: Apply the outer exponentiation:

Finally, we take the result of the previous step and raise it to the power of 3:

$4^3 = 64$

Therefore, the value of the expression $[(4-2)^2]^3$ is $64$.