Given x, is greater than, 0x>0 and y, is greater than, 0, commay>0, select the expression that is equivalent to

Question

square root of, minus, 36, x, to the power 6 , y, to the power 14 , end square root
−36x
6
y
14

​

Answer
Multiple Choice Answers
minus, 6, x, cubed, y, to the power 7−6x
3
y
7

minus, 6, x, to the power 12 , y, to the power 28−6x
12
y
28

6, i, x, to the power 12 , y, to the power 286ix
12
y
28

6, i, x, cubed, y, to the power 76ix
3
y
7

Answer 1

To simplify the expression \(\sqrt{-36x^6y^{14}}\), we first observe the components:

1. The coefficient \(-36\) can be factored out into \(-1\) and \(36\).
2. The square root of \(36\) is \(6\).
3. The square root of \(x^6\) is \(x^3\).
4. The square root of \(y^{14}\) is \(y^7\).

So we can rewrite the expression as:

\[ \sqrt{-36x^6y^{14}} = \sqrt{-1} \cdot \sqrt{36} \cdot \sqrt{x^6} \cdot \sqrt{y^{14}} = i \cdot 6 \cdot x^3 \cdot y^7 = 6i x^3 y^7 \]

Thus, the expression that is equivalent to \(\sqrt{-36x^6y^{14}}\) is:

\[ 6i x^3 y^7 \]

Looking at the multiple choice answers, the correct answer is:

6i \(x^3\) \(y^7\).