Explanation

Explanation

Let's calculate:

= 3⁰ = 1

= 3¹ × 3² = 3 × 9 = 27

= 1 + 27 - 1/3

= 9

Explanation

Let's solve for x:

x/2 + x/3 + x/6 = 10

To add these fractions, find a common denominator (6):

3x/6 + 2x/6 + x/6 = 10

6x/6 = 10

x = 10

Explanation

Let's simplify the expression:

√25^(3x) = √(5²)^(3x) = √(5^(6x)) = 5^(3x)

Now, divide by 5^(6x-2):

5^(3x) / 5^(6x-2) = 5^(3x - 6x + 2) = 5^(-3x + 2)

For this to equal one of the given options (5, 10, 15), let's see if -3x + 2 = 1 (for 5¹ = 5):

-3x + 2 = 1

-3x = -1

x = 1/3

Then, 5^(-3(1/3) + 2) = 5¹ = 5

Explanation

Let's simplify the expression:

√(12 + 2√35)

This can be rewritten as:

√(7 + 5 + 2√(7 × 5))

= √(√7 + √5)²

= √7 + √5

Explanation

Let's evaluate the expression step by step:

1. Calculate 2022²:

2022² = 4,088,484

2. Calculate 1²:

1² = 1

3. Calculate 2022² - 1²:

4,088,484 - 1 = 4,088,483

4. Divide by 2021:

4,088,483 ÷ 2021 = 2023

Explanation

Let's calculate:

5! = 5 × 4 × 3 × 2 × 1 = 120

√120 + 1 

√121 = √11×11

= 11

Explanation

Given the equation and solution path:

5^x + 2 - 5x = 600

If we interpret it as 5^(x+2) - 5^x = 600 (based on your calculation):

5^(2+2) - 5^2 = 5^4 - 5^2 = 625 - 25 = 600

This calculation implies x = 2 fits perfectly if the equation is treated as 5^(x+2) - 5^x = 600.

The value of x is 2.

Explanation

= √(200 + 6 × 10 - 4)/ 16

= √(200 + 60 - 4)/ 16

= √(260 - 4)/ 16

= √(256)/ 16

= 16 / 16

= 1

Explanation

Let's break it down step by step:

1. (√9²+12²) = √(81+144) = √225 = 15

2. (-3)² = 9

3. 15 + 9 = 24

4. (-1 + 2 + 3) = 4, and 4³ = 64

5. 24 - 64 = -40

6. ³√-125 = -5 (since (-5)³ = -125)

7. -40 - (-5) = -40 + 5 = -35