IDNLearn.com is your go-to resource for finding answers to any question you have. Join our community to receive prompt and reliable responses to your questions from knowledgeable professionals.
Sagot :
To find the expression that is equivalent to [tex]\(\sqrt{\sqrt{\sqrt{x^{48}}}}\)[/tex], we need to simplify the given expression step by step. Let's break it down:
1. Start with the innermost radical:
[tex]\[ \sqrt{x^{48}} \][/tex]
Rewriting the square root as an exponent, we have:
[tex]\[ (x^{48})^{1/2} \][/tex]
This simplifies to:
[tex]\[ x^{48 \cdot \frac{1}{2}} = x^{24} \][/tex]
2. Next, we take the square root of [tex]\(x^{24}\)[/tex]:
[tex]\[ \sqrt{x^{24}} \][/tex]
Rewriting the square root as an exponent, we get:
[tex]\[ (x^{24})^{1/2} \][/tex]
This simplifies to:
[tex]\[ x^{24 \cdot \frac{1}{2}} = x^{12} \][/tex]
3. Finally, we take the square root of [tex]\(x^{12}\)[/tex]:
[tex]\[ \sqrt{x^{12}} \][/tex]
Rewriting the square root as an exponent, we get:
[tex]\[ (x^{12})^{1/2} \][/tex]
This simplifies to:
[tex]\[ x^{12 \cdot \frac{1}{2}} = x^{6} \][/tex]
Therefore, the expression [tex]\(\sqrt{\sqrt{\sqrt{x^{48}}}}\)[/tex] simplifies to [tex]\(x^6\)[/tex].
So, the correct answer is:
[tex]\[ (A) \, x^6 \][/tex]
1. Start with the innermost radical:
[tex]\[ \sqrt{x^{48}} \][/tex]
Rewriting the square root as an exponent, we have:
[tex]\[ (x^{48})^{1/2} \][/tex]
This simplifies to:
[tex]\[ x^{48 \cdot \frac{1}{2}} = x^{24} \][/tex]
2. Next, we take the square root of [tex]\(x^{24}\)[/tex]:
[tex]\[ \sqrt{x^{24}} \][/tex]
Rewriting the square root as an exponent, we get:
[tex]\[ (x^{24})^{1/2} \][/tex]
This simplifies to:
[tex]\[ x^{24 \cdot \frac{1}{2}} = x^{12} \][/tex]
3. Finally, we take the square root of [tex]\(x^{12}\)[/tex]:
[tex]\[ \sqrt{x^{12}} \][/tex]
Rewriting the square root as an exponent, we get:
[tex]\[ (x^{12})^{1/2} \][/tex]
This simplifies to:
[tex]\[ x^{12 \cdot \frac{1}{2}} = x^{6} \][/tex]
Therefore, the expression [tex]\(\sqrt{\sqrt{\sqrt{x^{48}}}}\)[/tex] simplifies to [tex]\(x^6\)[/tex].
So, the correct answer is:
[tex]\[ (A) \, x^6 \][/tex]
Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. Your questions find answers at IDNLearn.com. Thanks for visiting, and come back for more accurate and reliable solutions.