Which of the following radical expressions simplifies to the answer below?

Question

2x15y−−−√
2
𝑥
15
𝑦
(1 point)
Responses
56xy2−−−−√
5
6
𝑥
𝑦
2
5 square root of 6 x y squared end root
350x2y−−−−−√
3
50
𝑥
2
𝑦
3 square root of 50 x squared y end root
60x2y−−−−−√
60
𝑥
2
𝑦
square root of 60 x squared y end root
30x2y−−−−−√

Answer 1

To determine which radical expression is equivalent to \( \sqrt{2x^{15}y} \), let's simplify each of the provided options and see if any match \( \sqrt{2x^{15}y} \).

1. Option 1: \( \sqrt{56xy^2} \) \[ \sqrt{56xy^2} = \sqrt{56} \sqrt{x} \sqrt{y^2} = \sqrt{56} \cdot \sqrt{y^2} \cdot \sqrt{x} = \sqrt{56} \cdot y \cdot \sqrt{x} \] (No match, since 56 does not reduce to 2 and the \(x\) and \(y\) powers differ.)

2. Option 2: \( 5 \sqrt{6xy^2} \) \[ 5 \sqrt{6xy^2} = 5 \cdot \sqrt{6} \cdot \sqrt{x} \cdot \sqrt{y^2} = 5 \cdot \sqrt{6} \cdot \sqrt{x} \cdot y \] (No match.)

3. Option 3: \( 3 \sqrt{50x^2y} \) \[ 3 \sqrt{50x^2y} = 3 \cdot \sqrt{50} \cdot \sqrt{x^2} \cdot \sqrt{y} = 3 \cdot \sqrt{50} \cdot x \cdot \sqrt{y} \] (No match since \( \sqrt{50} \) is not the same as \( \sqrt{2} \).)

4. Option 4: \( \sqrt{60x^2y} \) \[ \sqrt{60x^2y} = \sqrt{60} \cdot \sqrt{x^2} \cdot \sqrt{y} = \sqrt{60} \cdot x \cdot \sqrt{y} = x \cdot \sqrt{60y} \] (No match.)

5. Option 5: \( \sqrt{30x^2y} \) \[ \sqrt{30x^2y} = \sqrt{30} \cdot \sqrt{x^2} \cdot \sqrt{y} = \sqrt{30} \cdot x \cdot \sqrt{y} \] (No match.)

After checking all the options, none of them simplify directly to \( \sqrt{2x^{15}y} \).

To simplify \( \sqrt{2x^{15}y} \) directly: \[ \sqrt{2x^{15}y} = \sqrt{2} \cdot \sqrt{x^{15}} \cdot \sqrt{y} = \sqrt{2} \cdot x^{7} \cdot x^{\frac{1}{2}} \cdot y^{\frac{1}{2}} = x^7 \sqrt{2xy} \]

Thus, none of the given radical expressions simplify to \( \sqrt{2x^{15}y} \).

Answer 2

Put the steps in order used to simplify the expression below.
28−−√+363−−√
(5 points)
Arrange responses in the correct order to answer the question. Select a response, navigate to the desired position and insert response at that position.

2⋅2⋅7−−−−−−√+33⋅3⋅7−−−−−−√

4⋅7−−−−√+39⋅7−−−−√

11--7–√

27–√+3⋅37–√

27–√+97–√

Answer 3

To simplify the expression \( \sqrt{28} + \sqrt{36} \), we can follow these steps in order. Here's the correct arrangement:

1. Step 1: \( \sqrt{28} + \sqrt{36} \)
   (Start with the original expression)

2. Step 2: \( 2 \cdot 2 \cdot 7 + 3 \cdot 3 \cdot 7 \)
   (Rewrite the square roots in terms of their prime factors: \( 28 = 4 \cdot 7 \) and \( 36 = 9 \))

3. Step 3: \( \sqrt{4 \cdot 7} + \sqrt{9 \cdot 4} \)
   (Factor out the perfect squares)

4. Step 4: \( 2 \sqrt{7} + 3 \cdot 6\sqrt{7} \)
   (This could also be expressed as \( \sqrt{36} = 6 \))

5. Step 5: \( 2 \sqrt{7} + 6 \sqrt{7} \)
   (Combine the terms)

6. Step 6: \( 8 \sqrt{7} \)
   (Final simplified form)

So, putting this in order based on your provided steps:

• Step 1: \( \sqrt{28} + \sqrt{36} \)
• Step 2: \( 2 \cdot 2 \cdot 7 + 3 \cdot 3 \cdot 7 \)
• Step 3: \( 4 \cdot \sqrt{7} + 6 \cdot \sqrt{7} \)
• Step 4: \( 8 \sqrt{7} \)

Now, if you're looking to directly select the responses you provided, the order based on their correctness would be:

1. \( 2 \cdot 2 \cdot 7 + 3 \cdot 3 \cdot 7 \)
2. \( 4 \cdot \sqrt{7} + 6 \cdot \sqrt{7} \)
3. \( (4 + 9) \sqrt{7} \)
4. \( 11 \sqrt{7} \)

You may want to match these steps with the options you have in an appropriate context, but the fundamental steps illustrated above outline how we would simplify the expression. Based on the options given by you, we have combined steps in a more simplified way to yield a clear result.

Answer 4

Which of these equations is correct?(1 point)
Responses
(5−3)6=1518
(
5
−
3
)
6
=
1
5
18
open paren 5 to the negative 3 power close paren to the 6th power is equal to the fraction with numerator 1 and denominator 5 to the 18th power
(35)−2=13−10
(
3
5
)
−
2
=
1
3
−
10
open paren 3 to the 5th power close paren to the negative 2 power is equal to the fraction with numerator 1 and denominator 3 to the negative 10 power
(22)4=26
(
2
2
)
4
=
2
6
open paren 2 squared close paren to the 4th power is equal to 2 to the 6th power
(83)2=89

Answer 5

Let's evaluate each of the provided equations to determine which one is correct.

1. Option 1: \( (5^{-3})^6 = \frac{1}{5^{18}} \)

   • Using the power of a power property \((a^m)^n = a^{m \cdot n}\), \[ (5^{-3})^6 = 5^{-18} \]
   • Which can be rewritten as: \[ 5^{-18} = \frac{1}{5^{18}} \]
   • This equation is correct.

2. Option 2: \( (3^5)^{-2} = \frac{1}{3^{-10}} \)

   • Again using the power of a power property, \[ (3^5)^{-2} = 3^{-10} \]
   • The right side, \(\frac{1}{3^{-10}} = 3^{10}\),
   • Therefore, \[ 3^{-10} \neq 3^{10} \]
   • This equation is incorrect.

3. Option 3: \( (2^2)^4 = 2^6 \)

   • Using the power of a power property, \[ (2^2)^4 = 2^{2 \cdot 4} = 2^8 \]
   • Therefore, \[ 2^8 \neq 2^6 \]
   • This equation is incorrect.

4. Option 4: \( (8^3)^2 = 8^9 \)

   • Using the power of a power property, \[ (8^3)^2 = 8^{3 \cdot 2} = 8^{6} \]
   • Therefore, \[ 8^{6} \neq 8^{9} \]
   • This equation is incorrect.

Thus, the only correct equation among the options provided is:

\( (5^{-3})^6 = \frac{1}{5^{18}} \).