Powers and Roots: Using parentheses

Identify the greater valueUsing powersExercises with fractionsThe perimeter of a squareUsing fractionsSolving the equationSolving an exerciseTrue / falseParentheses within parenthesesComplete the missing numbersSmall NumbersSolving the problem
Question 1

\( 2\times(\sqrt{36}+9)= \)

Question 2

Calculate and indicate the answer:

\( (5-2)^2-2^3 \)

Question 3

What is the result of the following power?

\( (\frac{2}{3})^3 \)

Question 4

\( (2+1\times2)^2= \)

Question 5

Calculate and indicate the answer:

\( (\sqrt{9}-\sqrt{4})^2\cdot4^2-5^1 \)

Examples with solutions for Powers and Roots: Using parentheses

Exercise #1

2×(36+9)= 2\times(\sqrt{36}+9)=

Video Solution

Step-by-Step Solution

Let's solve this problem step by step using the order of operations (PEMDAS: Parentheses, Exponents, Multiplication/Division, Addition/Subtraction):

1. First, let's focus on what's inside the parentheses: 36+9 \sqrt{36}+9

2. We need to evaluate the square root first:

  • 36=6 \sqrt{36} = 6 (because 6×6=36 6 \times 6 = 36 )

3. Now our expression looks like this: 2×(6+9) 2\times(6+9)

4. Next, we perform the addition inside the parentheses:

  • 6+9=15 6 + 9 = 15

5. Our expression is now: 2×15 2\times15

6. Finally, we perform the multiplication:

  • 2×15=30 2 \times 15 = 30

Therefore, 2×(36+9)=30 2\times(\sqrt{36}+9) = 30

This matches the provided correct answer of 30.

Answer

30

Exercise #2

Calculate and indicate the answer:

(5−2)2−23 (5-2)^2-2^3

Video Solution

Step-by-Step Solution

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)2−23=32−23=9−8=1 (5-2)^2-2^3 =3^2-2^3=9-8=1 Therefore, the correct answer is option C.

Answer

1

Exercise #3

What is the result of the following power?

(23)3 (\frac{2}{3})^3

Video Solution

Answer

827 \frac{8}{27}

Exercise #4

(2+1×2)2= (2+1\times2)^2=

Video Solution

Answer

16

Exercise #5

Calculate and indicate the answer:

(9−4)2⋅42−51 (\sqrt{9}-\sqrt{4})^2\cdot4^2-5^1

Video Solution

Answer

11

Question 1

Calculate and indicate the answer:

\( (10^2-2\cdot5):3^2 \)

Question 2

Calculate and indicate the answer:

\( (\sqrt{100}-\sqrt{9})^2:7 \)

Question 3

Calculate and indicate the answer:

\( 5:(13^2-12^2) \)

Question 4

Solve the following question:

\( 3-(5^2:5)^2+7^2= \)

Question 5

Solve the following question:

\( (4^2:8):2+3^2= \)

Exercise #6

Calculate and indicate the answer:

(102−2⋅5):32 (10^2-2\cdot5):3^2

Video Solution

Answer

10

Exercise #7

Calculate and indicate the answer:

(100−9)2:7 (\sqrt{100}-\sqrt{9})^2:7

Video Solution

Answer

7

Exercise #8

Calculate and indicate the answer:

5:(132−122) 5:(13^2-12^2)

Video Solution

Answer

15 \frac{1}{5}

Exercise #9

Solve the following question:

3−(52:5)2+72= 3-(5^2:5)^2+7^2=

Video Solution

Answer

27

Exercise #10

Solve the following question:

(42:8):2+32= (4^2:8):2+3^2=

Video Solution

Answer

10

Question 1

Solve the following question:

\( (18-10)^2+3^3= \)

Question 2

Calculate and indicate the answer:

\( (4^2+3^2):\sqrt{25} \)

Question 3

Calculate and indicate the answer:

\( (\sqrt{25}-2^2)^3+2^3 \)

Question 4

Calculate and indicate the answer:

\( 7:(5^2-\sqrt{16})\cdot3+\sqrt{3}\cdot\sqrt{3} \)

Question 5

Calculate and indicate the answer:

\( (3^2+2^2)^2:(\sqrt{256}-\sqrt{9})-\sqrt{9}\cdot\sqrt{9} \)

Exercise #11

Solve the following question:

(18−10)2+33= (18-10)^2+3^3=

Video Solution

Answer

91

Exercise #12

Calculate and indicate the answer:

(42+32):25 (4^2+3^2):\sqrt{25}

Video Solution

Answer

5

Exercise #13

Calculate and indicate the answer:

(25−22)3+23 (\sqrt{25}-2^2)^3+2^3

Video Solution

Answer

9

Exercise #14

Calculate and indicate the answer:

7:(52−16)⋅3+3⋅3 7:(5^2-\sqrt{16})\cdot3+\sqrt{3}\cdot\sqrt{3}

Video Solution

Answer

4

Exercise #15

Calculate and indicate the answer:

(32+22)2:(256−9)−9⋅9 (3^2+2^2)^2:(\sqrt{256}-\sqrt{9})-\sqrt{9}\cdot\sqrt{9}

Video Solution

Answer

4

Question 1

Indicate whether the equality is true or not.

\( (5^2+3):2^2=5^2+(3:2^2) \)

Exercise #16

Indicate whether the equality is true or not.

(52+3):22=52+(3:22) (5^2+3):2^2=5^2+(3:2^2)

Video Solution

Answer

Not true