1.

Charles, Zayeer, and Kali are trying to simplify 100023
.

Charles says the correct simplification is 10 because 1000=10⋅10⋅10
and 100023=10
.

Zayeer says that the correct simplification is 1000 because 1000=10⋅10⋅10→100023=10⋅10⋅10=1000
.

Kali says the correct simplification is 100 because 1000=10⋅10⋅10→100023=10⋅10=100
.

Who has the correct value?

(2 points)
Responses

none of them
none of them

Zayeer
Zayeer

Charles
Charles

Kali
Kali
Question 2
2.

Simplify 24335

(2 points)
24335
=
Question 3
3.

Write the radical form of the expression 2514

(2 points)
2514 =

Question 4
4.

What is the simplest form of 2512
?

(2 points)
Responses

25−−√
square root of 25

5
5

12.5
12.5

25−−√12
1 halfth root of 25
Question 5
5.

Rewrite the following expressions:

2712⋅2714

(2 points)
The combined expression is 27 to the power of
(write as a fraction)

1 answer

Let's address your questions one by one:

Question 1: Charles, Zayeer, and Kali are trying to simplify \( 100023 \).

  • Charles says \( 100023 = 10 \). This is incorrect.
  • Zayeer says \( 100023 = 1000 \). This is also incorrect.
  • Kali says \( 100023 = 100 \). This is incorrect as well.

The number \( 100023 \) is already in its simplest form; none of the simplifications provided by Charles, Zayeer, or Kali are correct.

Response: none of them


Question 2: To simplify \( 24335 \): This number is already in its simplest form in relation to basic operations, as it's just a number. If you're looking to factor or express this in another form (like prime factorization), you would need additional context.

If you simply need \( 24335 \) as it is, the answer is: Response: \( 24335 \)


Question 3: To write \( 2514 \) in radical form: The term can be expressed as \( \sqrt[14]{25} \) because it signifies the 14th root of 25.

Response: \( 2514 = \sqrt[14]{25} \)


Question 4: What is the simplest form of \( 2512 \)? The expression \( 2512 \) can be simplified to \( \sqrt{25^{12}} = 25^{6} \) since the square root of \( 25 \) gives \( 5 \), and you have \( 12/2 = 6 \) when dealing with exponents.

You can also express this as \( 5^{12} \) since \( 25 = 5^{2} \).

Response: \( 5^{6} \)


Question 5: Rewrite \( 2712 \cdot 2714 \): According to the laws of exponents, you would add the exponents when multiplying like bases.

\[ 2712 \cdot 2714 = 27^{12 + 14} = 27^{26} \]

Response: The combined expression is \( 27^{26} \)

If you have further inquiries or need clarification, feel free to ask!

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