Given x, is greater than, 0, commax>0, the expression start root, start index, 10, end index, x, to the power 109 , end root

Question

10

x
109

​
is equivalent to
Answer
Multiple Choice Answers
x, to the power 11 , start root, start index, 10, end index, x, to the power 10 , end rootx
11

10

x
10

​

x, to the power 10 , start root, start index, 10, end index, x, to the power 9 , end rootx
10

10

x
9

​

x, to the power 11x
11

x, to the power 10x
10

Answer 1

To simplify the given expression \( \sqrt[10]{x^{109}} \), we can apply the property of exponents.

The expression can be rewritten using exponent rules:

\[ \sqrt[10]{x^{109}} = x^{\frac{109}{10}} = x^{10.9} \]

Now let's see how this is represented among the given answer choices:

To match with the format provided in the options, let's express \( x^{10.9} \) more clearly.

1. Option A: \( x^{11} \sqrt[10]{x^{10}} \)

   • Simplifying: \( x^{11} \cdot \sqrt[10]{x^{10}} = x^{11} \cdot x^{\frac{10}{10}} = x^{11} \cdot x^{1} = x^{12} \), which is incorrect.

2. Option B: \( x^{10} \sqrt[10]{x^{9}} \)

   • Simplifying: \( x^{10} \cdot \sqrt[10]{x^{9}} = x^{10} \cdot x^{\frac{9}{10}} = x^{10 + 0.9} = x^{10.9} \), which matches.

3. Option C: \( x^{11x} \), which doesn't match.

4. Option D: \( x^{10x} \), which doesn't match.

Thus, the correct equivalent expression for \( \sqrt[10]{x^{109}} \) is:

Answer: \( x^{10} \sqrt[10]{x^{9}} \)