Powers and Roots: Solving the problem

The given mathematical expression is $10:2-2^2$.

According to the order of operations (often remembered by the acronym PEMDAS/BODMAS), we perform calculations in the following sequence:

• Parentheses/Brackets
• Exponents/Orders (i.e., powers and roots)
• Multiplication and Division (from left to right)
• Addition and Subtraction (from left to right)

In this expression, there are no parentheses, but there is an exponent: $2^2$. We calculate the exponent first:

$2^2 = 4$

Substituting back into the expression, we have:

$10:2-4$

Next, we perform the division from left to right. Here, ":" is interpreted as division:

$10 \div 2 = 5$

Now, substitute this back into the expression:

$5 - 4$

The final step is to perform the subtraction:

$5 - 4 = 1$

Therefore, the answer is $1$.

First, compute the power: $5^2 = 25$.

Next, divide: $25 \div 5 = 5$.

Finally, subtract: $10 - 5 = 5$.

First, compute the power: $4^2 = 16$.

Next, divide: $16 \div 2 = 8$.

Finally, subtract: $15 - 8 = 7$.

First, compute the power: $3^3 = 27$.

Next, divide: $27 \div 3 = 9$.

Finally, subtract: $20 - 9 = 11$.

First, evaluate the square root: $\sqrt{81}=9$.

Then, follow the order of operations (PEMDAS/BODMAS):

1. Multiplication: $3 \times 2 = 6$

2. Addition: $6 + 9 = 15$

So, the correct answer is $15$.

First we need to remind ourselves of the order of operations:

1. Parentheses

2. Exponents and Roots

3. Multiplication and Division

4. Addition and Subtraction

There are no parentheses in this problem, therefore we will start with exponents:

3 * 3 + 3² =

3 * 3 + 9 =

Let's continue to the next step—multiplication operations:

3 * 3 + 9 =

9 + 9 =

Finally, we are left with a simple addition exercise:

9 + 9 = 18

To solve the expression $4 + 2^2$, follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)).

Let's break down the expression:

• Step 1: Identify any exponents.
  The expression contains an exponent: $2^2$. To evaluate this, multiply 2 by itself: $2 \times 2$, which equals 4.
  So, $2^2 = 4$.
• Step 2: Perform addition.
  Now, substitute the result back into the original expression:
  $4 + 4$.
  Add these numbers together: 4 + 4 equals 8.

Therefore, the answer to the expression $4 + 2^2$ is 8.

To solve the expression $4 + 2 + 5^2$, we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

• Step 1: Calculate Exponents
  In the expression we have an exponent: $5^2$. This means 5 is raised to the power of 2. We calculate this first:
  $5^2 = 25$.


• Step 2: Perform Addition
  Now, substitute the calculated value back into the expression:
  $4 + 2 + 25$.
  Perform the additions from left to right:
  $4 + 2 = 6$
  Finally add the result to 25:
  $6 + 25 = 31$.

First, solve the square root: $\sqrt{49} = 7$.

Next, multiply 7 by 3: $7 \times 3 = 21$.

Finally, add 4 to 21: $4 + 21 = 25$.

Start by calculating the power: $5^2 = 25$.

Then, calculate the square root: $\sqrt{16} = 4$.

Subtract 4 from 25: $25 - 4 = 21$.

Finally, add 2: $21 + 2 = 23$.

To solve the expression $5+\sqrt{36}-1=$, we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction).

Here are the steps:

First, calculate the square root:

$\sqrt{36} = 6$

Substitute the square root back into the expression:

$5 + 6 - 1$

Next, perform the addition and subtraction from left to right:

Add 5 and 6:

$5 + 6 = 11$

Then subtract 1:

$11 - 1 = 10$

Finally, you obtain the solution:

$10$

First, follow the order of operations (BODMAS/BIDMAS):

Step 1: Calculate the exponent:
$2^2 = 4$

Step 2: Perform the multiplication:
$5 \times 4 = 20$

Step 3: Perform the addition and subtraction from left to right:
$6 - 3 + 20 = 23$

The correct result is: $23$.

To solve the expression $6+\sqrt{64}-4=$, we need to follow the order of operations (PEMDAS/BODMAS):

• P: Parentheses (or Brackets)
• E: Exponents (or Orders, i.e., powers and roots, etc.)
• MD: Multiplication and Division (left-to-right)
• AS: Addition and Subtraction (left-to-right)

In this expression, we first need to evaluate the square root since it falls under the exponent category:

$\sqrt{64} = 8$

Next, we substitute the computed value back into the expression:

$6+8-4$

We then perform the addition and subtraction from left to right:

$6+8 = 14$

$14-4 = 10$

Thus, the final answer is:

$10$

First, evaluate the square root: $\sqrt{49}=7$.

Then, follow the order of operations (PEMDAS/BODMAS):

1. Addition: $7 + 7 = 14$

2. Subtraction: $14 - 5 = 9$

So, the correct answer is $9$.

Let's solve the expression step by step using the order of operations, often remembered by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).

The given expression is: $8-3^2:3=$

Step 1: Evaluate Exponents
The expression has an exponent, which we need to evaluate first. The exponent is $3^2$.
Calculate $3^2$ which equals $9$.
Now the expression becomes: $8 - 9 : 3$

Step 2: Division
Next, perform the division operation. Here we divide $9$ by $3$.
Calculate $9 : 3$ which equals $3$.
Now the expression becomes: $8 - 3$

Step 3: Subtraction
Finally, perform the subtraction.
Calculate $8 - 3$ which equals $5$.

Therefore, the solution to the expression $8-3^2:3$ is $5$.

First, follow the order of operations (BODMAS/BIDMAS):

Step 1: Calculate the exponent:
$4^2 = 16$

Step 2: Perform the multiplication:
$3 \times 2 = 6$

Step 3: Perform the addition and subtraction from left to right:
$8 + 6 - 16 = 14 - 16 = -2$

The correct result is: $-2$.

First, evaluate the square root: $\sqrt{16}=4$.

Then, follow the order of operations (PEMDAS/BODMAS):

1. Multiplication: $4 \times 3 = 12$

2. Subtraction: $8 - 12 = -4$

So, the correct answer is $-4$.

To solve the expression, we need to follow the order of operations, often remembered by the acronym PEMDAS, which stands for Parentheses, Exponents, Multiplication and Division (left-to-right), Addition and Subtraction (left-to-right).

• Step 1: Handle the exponentiation in the expression.
  The exponentiation operation is on the number 2, so we compute $2^2$ which is equal to 4.
• Step 2: Handle the multiplication.
  We multiply the result of the exponentiation by the number following it. Therefore, we have $4 \times 1^{10}$. Since $1^{10} = 1$, the expression becomes $4 \times 1 = 4$.
• Step 3: Handle the operations on either side of multiplication.
  Before evaluating, it's essential to note that the original expression is slightly misunderstood due to potential formatting errors. Let's assume it was meant to use division as $0 \div 2^2$ due to the notation $0:2^2$. Therefore, calculate $0 \div 4$ which is equal to 0.
• Step 4: Handle the addition.
  Finally, we add 3 to the result of the division: $0 + 3 = 3$.

Thus, the final answer is 3.

To solve the expression $100:5^2+3^2=$, we need to follow the order of operations, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)). Here, we have division, exponentiation, and addition to work with.

Step 1: Calculate the exponentiation first.

• Calculate $5^2$: $5 \times 5 = 25$.
• Calculate $3^2$: $3 \times 3 = 9$.

So, the expression becomes $100:25+9$.

Step 2: Perform the division next, which comes before addition.

• Divide $100$ by $25$: $100 \div 25 = 4$.

Now the expression simplifies to $4 + 9$.

Step 3: Perform the addition.

• Add $4$ and $9$: $4 + 9 = 13$.

Therefore, the final result of the expression $100:5^2+3^2$ is $13$.

To solve the expression $143-\sqrt{121}+18$, we need to follow the order of operations, which dictate that we should simplify any expressions under a square root first, followed by subtraction and addition.

Step 1: Simplify the square root:

• Calculate the square root: $\sqrt{121}$.
• The square root of 121 is 11, because $11 \times 11 = 121$.

Now, substitute back into the expression:

• The expression becomes: $143 - 11 + 18$.

Step 2: Perform the subtraction:

• Calculate $143 - 11$.
• This equals 132, because subtracting 11 from 143 yields 132.

Step 3: Perform the addition:

• Now add 18 to the result of the subtraction: $132 + 18$.
• The result is 150, because adding 18 to 132 equals 150.

Therefore, the final answer is $150$.