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Answer :
Let's simplify the expression [tex]\(\sqrt[1]{625 x^{12}}\)[/tex].
It seems like you meant to write [tex]\(\sqrt{625 x^{12}}\)[/tex].
Here's how you simplify it step-by-step:
1. Understand the Expression:
[tex]\(\sqrt{625 x^{12}}\)[/tex] is looking for the square root of both 625 and [tex]\(x^{12}\)[/tex].
2. Square Root of 625:
- The square root of 625 is 25 because [tex]\(25 \times 25 = 625\)[/tex].
3. Square Root of [tex]\(x^{12}\)[/tex]:
- To find the square root of [tex]\(x^{12}\)[/tex], apply the rule [tex]\((a^b)^{1/2} = a^{b/2}\)[/tex].
- Therefore, [tex]\(\sqrt{x^{12}} = x^{12/2} = x^6\)[/tex].
4. Combine the Results:
- Combine the results of both square roots: [tex]\(25\)[/tex] from 625 and [tex]\(x^6\)[/tex] from [tex]\(x^{12}\)[/tex].
- Therefore, [tex]\(\sqrt{625 x^{12}} = 25x^6\)[/tex].
The simplified expression is [tex]\(25x^6\)[/tex].
It seems like you meant to write [tex]\(\sqrt{625 x^{12}}\)[/tex].
Here's how you simplify it step-by-step:
1. Understand the Expression:
[tex]\(\sqrt{625 x^{12}}\)[/tex] is looking for the square root of both 625 and [tex]\(x^{12}\)[/tex].
2. Square Root of 625:
- The square root of 625 is 25 because [tex]\(25 \times 25 = 625\)[/tex].
3. Square Root of [tex]\(x^{12}\)[/tex]:
- To find the square root of [tex]\(x^{12}\)[/tex], apply the rule [tex]\((a^b)^{1/2} = a^{b/2}\)[/tex].
- Therefore, [tex]\(\sqrt{x^{12}} = x^{12/2} = x^6\)[/tex].
4. Combine the Results:
- Combine the results of both square roots: [tex]\(25\)[/tex] from 625 and [tex]\(x^6\)[/tex] from [tex]\(x^{12}\)[/tex].
- Therefore, [tex]\(\sqrt{625 x^{12}} = 25x^6\)[/tex].
The simplified expression is [tex]\(25x^6\)[/tex].
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