At Westonci.ca, we connect you with the answers you need, thanks to our active and informed community. Get the answers you need quickly and accurately from a dedicated community of experts on our Q&A platform. Get quick and reliable solutions to your questions from a community of experienced experts on our platform.
Sagot :
To determine which expression is equivalent to [tex]\(\left(64 y^{100}\right)^{\frac{1}{2}}\)[/tex], we can follow these steps:
1. Understand the expression: We have the expression [tex]\(\left(64 y^{100}\right)^{\frac{1}{2}}\)[/tex].
2. Apply the exponent outside the parenthesis: We need to distribute the [tex]\(\frac{1}{2}\)[/tex] exponent to both the numerical coefficient (64) and the variable part ([tex]\(y^{100}\)[/tex]) separately.
3. Simplifying the numerical part:
- Calculate [tex]\((64)^{\frac{1}{2}}\)[/tex].
- The square root of 64 ([tex]\((64)^{\frac{1}{2}}\)[/tex]) is 8.
4. Simplifying the variable part:
- Calculate [tex]\((y^{100})^{\frac{1}{2}}\)[/tex].
- Use the power rule [tex]\((a^m)^n = a^{m \cdot n}\)[/tex]:
[tex]\[(y^{100})^{\frac{1}{2}} = y^{100 \cdot \frac{1}{2}} = y^{50}.\][/tex]
5. Combine the simplified parts:
- Multiply the results together: [tex]\(8 \cdot y^{50}\)[/tex].
So, the equivalent expression is [tex]\(8 y^{50}\)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{8 y^{50}}. \][/tex]
1. Understand the expression: We have the expression [tex]\(\left(64 y^{100}\right)^{\frac{1}{2}}\)[/tex].
2. Apply the exponent outside the parenthesis: We need to distribute the [tex]\(\frac{1}{2}\)[/tex] exponent to both the numerical coefficient (64) and the variable part ([tex]\(y^{100}\)[/tex]) separately.
3. Simplifying the numerical part:
- Calculate [tex]\((64)^{\frac{1}{2}}\)[/tex].
- The square root of 64 ([tex]\((64)^{\frac{1}{2}}\)[/tex]) is 8.
4. Simplifying the variable part:
- Calculate [tex]\((y^{100})^{\frac{1}{2}}\)[/tex].
- Use the power rule [tex]\((a^m)^n = a^{m \cdot n}\)[/tex]:
[tex]\[(y^{100})^{\frac{1}{2}} = y^{100 \cdot \frac{1}{2}} = y^{50}.\][/tex]
5. Combine the simplified parts:
- Multiply the results together: [tex]\(8 \cdot y^{50}\)[/tex].
So, the equivalent expression is [tex]\(8 y^{50}\)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{8 y^{50}}. \][/tex]
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.