Question

which of the following represents \\(\sqrt9{x^7}\\) in exponential form?

\\(x^{\frac{9}{7}}\\)

\\(x^{\frac{7}{9}}\\)

\\(9x^7\\)

\\(7x^9\\)

question 8 (multiple choice worth 6 points)
(01.08r hc)

find the volume of a rectangular prism if the length is \\(4x\\), the width is \\(2x\\), and the height is \\(x^3 + 3x + 6\\). use the formula \\(v = l \cdot w \cdot h\\), where \\(l\\) is length, \\(w\\) is width, and \\(h\\) is height, to find the volume.

\\(6x^5 + 18x^3 + 36x^2\\)

\\(6x^6 + 18x^3 + 36x^2\\)

\\(8x^5 + 24x^3 + 48x^2\\)

\\(8x^6 + 24x^3 + 48x^2\\)

Explanation:

Convert radical to exponential form

$$ \sqrt[9]{x^7} = x^{\frac{7}{9}} $$

Multiply length and width

$$ l \cdot w = (4x) \cdot (2x) = 8x^2 $$

Multiply by height to find volume

$$ V = (8x^2) \cdot (x^3 + 3x + 6) = 8x^5 + 24x^3 + 48x^2 $$

Answer:

Question 1

• (A) \(x^{\frac{9}{7}}\)
• (B) \(x^{\frac{7}{9}}\) (Correct answer)
• (C) \(9x^7\)
• (D) \(7x^9\)

Question 2

• (A) \(6x^5 + 18x^3 + 36x^2\)
• (B) \(6x^6 + 18x^3 + 36x^2\)
• (C) \(8x^5 + 24x^3 + 48x^2\) (Correct answer)
• (D) \(8x^6 + 24x^3 + 48x^2\)