1.

Question

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)
Question 6
6.

What is an equivalent expression for −(b14)12
?

(2 points)
Responses

−b−3
negative b to the negative 3 power

−b3
negative b cubed

1b3
the fraction with numerator 1 and denominator b cubed

−1b3
negative the fraction with numerator 1 and denominator b cubed
Question 7
7.

Find the value of x.

−x32=−27

(2 points)
x=

Question 8
8.

Solve for x.

27x34−1=26

(2 points)
x=

Question 9
9.

Using exponent properties, which of the following expressions is equivalent to (2–√)3⋅2−12
?

(2 points)
Responses

212
2 raised to the 1 half power

2–√
square root of 2

2
2

22
2 squared
Question 10
10.

When applying the exponent properties, what is the equivalent expression to 216√32713
?

(2 points)
the equivalent expression is:
Question 11
11.

The equation (8–√4)−24⋅(8–√)16=8−48
is false. Select the responses that explain what was done incorrectly.

(4 points)
The equation is false because the exponents should be
rather than
Question 12
12.

Simplify the expression

7−4⋅7349√

(2 points)
The simplified expression is
(do not include negative exponents) (Answer should be a simplified fraction)
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Answer 1

Let's tackle each question step by step:

Question 1: Who has the correct value for simplifying \(100023\)?

The value \(100023\) can be interpreted in terms of its factors of 10 and represents \(1000^2\) as it has a clear structure of 10 to the power of 6 (since \(1000000 = 10^6\)). Hence:

• Charles's interpretation of \(100023 = 10\) is incorrect.
• Zayeer's interpretation of \(100023 = 1000\) is incorrect. He confuses bases.
• Kali's interpretation of \(100023 = 100\) is also incorrect.

Thus, none of them is correct.

Question 2: Simplify \(24335\).

To simplify this number, we factor it: \[ 24335 = 5 \times 4867 \] The number cannot be simplified further easily without a specific request for factors or primes.

So the answer remains as \(24335\).

Question 3: Write the radical form of the expression \(2514\).

This means expressing it as: \[ 2514 = 25^{7} = (5^2)^{14} = 5^{28} \] The radical form is not explicitly to show this. However, it depends on using rational roots as well, which were not clearly asked for.

Thus, \(2514 = \sqrt[14]{25^2}\) makes sense in this interpretation: \[ = \sqrt[14]{25^{14}} = 25 \text{ (since the exponent and the root match)} \]

Question 4: What is the simplest form of \(2512\)?

\[ 25^{12} = 5^{24} \text{ or } \sqrt{5^{24}} = 5^{12} \] The simplest form is \(5^{12}\).

Question 5: Rewrite the expressions \(2712 \cdot 2714\).

Using the property of exponents: \[ a^m \cdot a^n = a^{m+n} \] So we get: \[ 27^{12+14} = 27^{26} \]

Question 6: What is an equivalent expression for \(- (b^{14})^{12}\)?

Using power of a power: \[

• (b^{14})^{12} = - b^{168} \] None of the responses given fits perfectly, but \(- b^{168}\) would be correct.

Question 7: Find the value of \(x\) in \(-x^{32} = -27\).

Removing negatives from both sides gives: \[ x^{32} = 27 \implies x = 27^{1/32} \]

Question 8: Solve for \(x\) in \(27x^{34} - 1 = 26\).

Adding to both sides: \[ 27x^{34} = 27 \implies x^{34} = 1 \implies x = 1 \text{ or } -1 \]

Question 9: Using exponent properties, which of the following expressions is equivalent to \((2^{-\frac{1}{2}})^{3} \cdot 2^{-1}\)?

First calculate: \[ (2^{-\frac{1}{2}})^{3} = 2^{-\frac{3}{2}} \]

Then multiply: \[ = 2^{-\frac{3}{2} - 1} = 2^{- \frac{5}{2}} \text{ or } \frac{1}{\sqrt{2^5}} = 2^{-\frac{5}{2}} \]

Question 10: What is the equivalent expression to \(216\sqrt{32713}\)?

216 becomes \(6^3\), and \(\sqrt{32713}\) doesn't simplify easily without values.

Question 11: The equation \((8\sqrt{4})^{-2} \cdot (8\sqrt{})^{16} = 8^{-48}\) is false.

Thus, your explanation text must point at exponents.

Question 12: Simplify the expression \(7^{-4} \cdot 7349\).

Using exponent properties, this results in a fraction form without negatives left in the final form.

If you have any question or need further details on any specific solution, feel free to ask!