Question

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) 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 simplified form of the expression 216√32713 ?(2 points) The simplified form of the 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) Skip to navigation

Answer 1

Let's go through each of the questions systematically.

Question 1:

Who has the correct value among Charles, Zayeer, and Kali regarding the simplification of \(100023\)?

• Charles states \(1000 = 10^3\) and \(100023 = 10^1\), which is incorrect.
• Zayeer states \(1000 = 10^3\) and simplistically calculates \(100023 = 10 \cdot 10 \cdot 10 = 1000\), which is incorrect in context.
• Kali deduces \(1000 = 10^3\) and simplifies \(100023\) to be \(10 \cdot 10 = 100\), which again is incorrect.

Correct Value: None of them.

Question 2:

Simplify \(24335\)

Since \(24335\) is not conducive to simplification as the number itself, it's likely meant to be interpreted as \(2^4 \cdot 3^3 \cdot 5^5\). Thus,

Answer: \(24335\) simplified is \(2^4 \cdot 3^3 \cdot 5^5\) or you would typically state it as is.

Question 3:

Write the radical form of the expression \(2514\):

The radical form of \(25^{14}\) can be written as: \[ (5^2)^{14} = 5^{28} \] But the simplest radical form of this expression does not apply if treated directly.

Answer: \( (5^{28}) \)

Question 4:

What is the simplest form of \(2512\)?

This means \((25^{12})\), and since \(25 = 5^2\): \[ (5^2)^{12} = 5^{24} \] The square root of \(25\) reduces to \(5^{12}\), and thus.

Answer: \(5^{12}\)

Question 5:

Rewrite the following expression \(2712 \cdot 2714\):

Using properties of exponents, add the exponents: \[ 27^{12} \cdot 27^{14} = 27^{12+14} = 27^{26} \] So, Answer: \(27^{26}\)

Question 6:

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

Using the power of a power property: \[ -(b^{14})^{12} = -b^{168} = -b^{(-168)} \]

Answer: \(-b^{168}\)

Question 7:

Find the value of \(x\) in \(−x^{32} = −27\):

Removing the negative sign via division: \[ x^{32} = 27 \quad \Rightarrow \quad x = 27^{1/32} \] Since \(27 = 3^3\): \[ x = 3^{3/32} \]

Question 8:

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

Rearranging gives: \[ 27x^{34} = 27 \quad \Rightarrow \quad x^{34} = 1 \ x = 1^{1/34} = 1 \]

Question 9:

Using exponent properties, which of the following expressions is equivalent to \((2^{-1/2})^3 \cdot 2^{-12}\):

Expanding: \[ (2^{-1/2})^3 = 2^{-3/2} \] Adding the exponents: \[ 2^{-3/2} \cdot 2^{-12} = 2^{-3/2 - 12} = 2^{-27/2} \]

Question 10:

What is the simplified form of the expression \(2^{16} \sqrt{3^{27} 17^{13}}\)?

Simplifying \( \sqrt{3^{27} 17^{13}} \) gives \(3^{27/2} \cdot 17^{13/2}\) and overall we have: \[ 2^{16} \cdot 3^{13.5} \cdot 17^{6.5} \]

Question 11:

Explanation of the mathematics in \( (8 - \sqrt{4})^{-24} \cdot (8 - \sqrt{})^{16} = 8^{-48}\)

The equation isn’t justified. Needs checking of exponents combined/mistake in simplification.

Question 12:

Simplify the expression \(7^{-4}\cdot 7349\sqrt{}\):

Use properties of exponentials: \[ \text{That would require direct calculation. } \] Since answer formatting isn't visible, it would be approached individually.

These are the refined approaches for each question. Let me know if you need any clarifications!