All Operations in the Order of Operations: Using parentheses

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

$7\times1=7$

Resulting in the following expression:

$8\times7=56$

According to the order of operations, we first solve the expression in parentheses:

$5\times1=5$

Now we multiply:

$8\times5=40$

First, calculate the expression within the parentheses:

$2 \times 1 = 2$

Now, multiply the result by 9:

$9 \times 2 = 18$

Thus, the final answer is 18.

Let's start with the part inside the parentheses. 

$2+2=4$
Then we will solve the exercise from left to right 

$8:2=4$
$4 × (4)=16$

The answer: $16$

The problem to be solved is $0.6\times(1+2)=$. Let's go through the solution step by step, following the order of operations.

Step 1: Evaluate the expression inside the parentheses.
Inside the parentheses, we have $1+2$. According to the order of operations, we first solve expressions in parentheses. Thus, we have:

$1 + 2 = 3$

So, the expression simplifies to $0.6\times3$.

Step 2: Perform the multiplication.
With the parentheses removed, we now carry out the multiplication:

$0.6 \times 3 = 1.8$

Thus, the final answer is $1.8$.

To solve the expression $\frac{1}{3}+(2-1)$, we need to follow the order of operations, often abbreviated as PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). This problem primarily involves parentheses and addition.

We'll start by solving the expression within the parentheses:

• The expression inside the parentheses is $(2-1)$. Subtracting, we get:

$2 - 1 = 1$

After solving the parentheses, the expression becomes:

$\frac{1}{3} + 1$

Next, we perform the addition:

• Since $1$ can be written as $\frac{3}{3}$ to have a common denominator with $\frac{1}{3}$, we add:

$\frac{1}{3} + \frac{3}{3} = \frac{1+3}{3} = \frac{4}{3}$

The fraction $\frac{4}{3}$ can also be expressed as a mixed number:

• $\frac{4}{3} = 1 \frac{1}{3}$ (where $1$ is the whole number and $\frac{1}{3}$ is the fractional part)

Thus, the correct answer is $1\frac{1}{3}$.

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

$1-1=0$

And we get the expression:

$0.18+0=0.18$

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

$19-1=18$

We obtain the following expression:

$0\times18+2=$

According to the order of operations, we'll multiply first and then add:

$0\times18=0$

$0+2=2$

According to the order of operations, we first solve the expression in parentheses:

$18-0=18$

Now we divide:

$18:3=6$

First, calculate the expression inside the parentheses: $3 + 1$ equals $4$.

Then multiply $0.4$ by $4$ to get $1.6$.

We solve the exercise in parentheses:$3\cdot3+5:1=$

We place in parentheses the multiplication and division exercises:

$(3\cdot3)+(5:1)=$

We solve the exercises in parentheses:

$9+5=14$

First, we solve the exercise within the parentheses:

$4\cdot2-3:4=$

We place multiplication and division exercises within parentheses:

$(4\cdot2)-(3:4)=$

We solve the exercises within the parentheses:

$8-\frac{3}{4}=7\frac{1}{4}$

We solve the exercise in parentheses:

$3:9\cdot9-6=$

$\frac{3}{9}\cdot9-6=$

We simplify and subtract:

$3-6=-3$

To solve the given power expression, we need to apply the formula for powers of a fraction. The expression we are given is:
$\left(\frac{2}{3}\right)^3$

Let's break down the steps:

• When we raise a fraction to a power, we apply the exponent to both the numerator and the denominator separately. This means raising both 2 and 3 to the power of 3.
• Thus, we calculate:
  $2^3 = 8$ and $3^3 = 27$.
• Therefore, $\left(\frac{2}{3}\right)^3 = \frac{2^3}{3^3} = \frac{8}{27}$.

So, the result of the expression $\left(\frac{2}{3}\right)^3$ is $\frac{8}{27}$.

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:

$6-4.5=1.5$

Remember that according to the order of arithmetic operations, exponents precede multiplication and division, which precede addition and subtraction (and parentheses always precede everything).

So first calculate the values of the terms with exponents and then subtract the results:

$(5-2)^2-2^3 =3^2-2^3=9-8=1$Therefore, the correct answer is option C.

Previously mentioned in the order of operations that exponents come before multiplication and division which come before addition and subtraction (and parentheses always come before everything),

Let's calculate then first the value of the expression inside the parentheses (by calculating the roots inside the parentheses first) :

$(\sqrt{9}-\sqrt{4})^2\cdot4^2-5^1 =(3-2)^2\cdot4^2-5^1 =1^2\cdot4^2-5^1$where in the second stage we simplified the expression in parentheses,

Next we'll calculate the values of the terms with exponents:

$1^2\cdot4^2-5^1 =1\cdot16-5$then we'll calculate the results of the multiplications

$1\cdot16-5 =16-5$and after that we'll perform the subtraction:

$16-5=11$Therefore the correct answer is answer B.

Previously mentioned in the order of operations that exponents come before multiplication and division which come before addition and subtraction (and parentheses always come before everything),

Let's calculate first the value of the expression inside the parentheses (by calculating the values of the terms inside the parentheses first) :

$(10^2-2\cdot5):3^2 = (100-10):3^2 =90:3^2=\frac{90}{3^2}$where in the second stage we simplified the expression in parentheses, and in the next stage we wrote the division operation as a fraction,

Next we'll calculate the value of the term in the fraction's numerator by performing the exponent, and in the next stage we'll perform the division (essentially reducing the fraction):

$\frac{90}{3^2} =\frac{\not{90}}{\not{9}}=10$Therefore the correct answer is answer D.

Previously mentioned in the order of arithmetic operations, exponents come before multiplication and division which come before addition and subtraction (and parentheses always come before everything),

Let's calculate first the value of the expression inside the parentheses (by calculating the values of the root terms inside the parentheses first) :

$(\sqrt{100}-\sqrt{9})^2:7 = (10-3)^2:7 =7^2:7=\frac{7^2}{7}$where in the second step we simplified the expression in parentheses, and in the next step we wrote the division operation as a fraction,

Next we'll calculate the value of the numerator by performing the exponentiation, and in the next step we'll perform the division (essentially reducing the fraction):

$\frac{7^2}{7} =\frac{\not{49}}{\not{7}}=7$Therefore the correct answer is answer A.

Previously mentioned in the order of arithmetic operations, exponents come before multiplication and division which come before addition and subtraction (and parentheses always come before everything),

Let's calculate first the value of the expression inside the parentheses (by calculating the values of the terms with exponents inside the parentheses first) :

$5:(13^2-12^2) =5:(169-144) =5:25=\frac{5}{25}$where in the second step we simplified the expression in parentheses, and in the next step we wrote the division operation as a fraction,

Then we'll perform the division (we'll actually reduce the fraction):

$\frac{\not{5}}{\not{25}}=\frac{1}{5}$Therefore the correct answer is answer C.