Find the best answers to your questions at Westonci.ca, where experts and enthusiasts provide accurate, reliable information. Connect with a community of experts ready to help you find solutions to your questions quickly and accurately. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.
Sagot :
We need to identify which of these statements correctly apply the negative exponent property. The negative exponent property states that [tex]\(a^{-b} = \frac{1}{a^b}\)[/tex].
Let's evaluate each statement individually:
1. [tex]\(17^{-\frac{1}{4}} = \frac{1}{17^{\frac{1}{4}}}\)[/tex]
- This is a correct application of the negative exponent property. For any positive number [tex]\(a\)[/tex] and any positive real number [tex]\(b\)[/tex], [tex]\(a^{-b} = \frac{1}{a^b}\)[/tex]. Thus, [tex]\(17^{-\frac{1}{4}} = \frac{1}{17^{\frac{1}{4}}}\)[/tex].
2. [tex]\(6^{-\frac{1}{3}} = -6^{\frac{1}{3}}\)[/tex]
- This statement is incorrect. According to the negative exponent property, it should be [tex]\(6^{-\frac{1}{3}} = \frac{1}{6^{\frac{1}{3}}}\)[/tex], not [tex]\(-6^{\frac{1}{3}}\)[/tex].
3. [tex]\(y^{\frac{1}{2}} = \frac{1}{y^{\frac{1}{2}}}\)[/tex]
- This statement is incorrect. The expression [tex]\(y^{\frac{1}{2}}\)[/tex] represents the square root of [tex]\(y\)[/tex]. The correct application of the negative exponent property would be [tex]\(\frac{1}{y^{\frac{1}{2}}}\)[/tex] or [tex]\(y^{-\frac{1}{2}} = \frac{1}{y^{\frac{1}{2}}}\)[/tex].
4. [tex]\(8^{-\frac{1}{6}} = -\frac{1}{8^{\frac{1}{8}}}\)[/tex]
- This statement is incorrect. According to the negative exponent property, it should be [tex]\(8^{-\frac{1}{6}} = \frac{1}{8^{\frac{1}{6}}}\)[/tex], not [tex]\(-\frac{1}{8^{\frac{1}{8}}}\)[/tex].
5. [tex]\(x^{-\frac{1}{7}} = \frac{x}{x^{\frac{3}{7}}}\)[/tex]
- This statement is incorrect. The correct application of the negative exponent property would produce [tex]\(x^{-\frac{1}{7}} = \frac{1}{x^{\frac{1}{7}}}\)[/tex].
To summarize, the two statements that correctly apply the negative exponent property are:
- [tex]\(17^{-\frac{1}{4}}=\frac{1}{17^{\frac{1}{4}}}\)[/tex]
Thus, the correct answer is:
[tex]\(\bigcirc \, 17^{-\frac{1}{4}}=\frac{1}{17^{\frac{1}{4}}}\)[/tex]
Let's evaluate each statement individually:
1. [tex]\(17^{-\frac{1}{4}} = \frac{1}{17^{\frac{1}{4}}}\)[/tex]
- This is a correct application of the negative exponent property. For any positive number [tex]\(a\)[/tex] and any positive real number [tex]\(b\)[/tex], [tex]\(a^{-b} = \frac{1}{a^b}\)[/tex]. Thus, [tex]\(17^{-\frac{1}{4}} = \frac{1}{17^{\frac{1}{4}}}\)[/tex].
2. [tex]\(6^{-\frac{1}{3}} = -6^{\frac{1}{3}}\)[/tex]
- This statement is incorrect. According to the negative exponent property, it should be [tex]\(6^{-\frac{1}{3}} = \frac{1}{6^{\frac{1}{3}}}\)[/tex], not [tex]\(-6^{\frac{1}{3}}\)[/tex].
3. [tex]\(y^{\frac{1}{2}} = \frac{1}{y^{\frac{1}{2}}}\)[/tex]
- This statement is incorrect. The expression [tex]\(y^{\frac{1}{2}}\)[/tex] represents the square root of [tex]\(y\)[/tex]. The correct application of the negative exponent property would be [tex]\(\frac{1}{y^{\frac{1}{2}}}\)[/tex] or [tex]\(y^{-\frac{1}{2}} = \frac{1}{y^{\frac{1}{2}}}\)[/tex].
4. [tex]\(8^{-\frac{1}{6}} = -\frac{1}{8^{\frac{1}{8}}}\)[/tex]
- This statement is incorrect. According to the negative exponent property, it should be [tex]\(8^{-\frac{1}{6}} = \frac{1}{8^{\frac{1}{6}}}\)[/tex], not [tex]\(-\frac{1}{8^{\frac{1}{8}}}\)[/tex].
5. [tex]\(x^{-\frac{1}{7}} = \frac{x}{x^{\frac{3}{7}}}\)[/tex]
- This statement is incorrect. The correct application of the negative exponent property would produce [tex]\(x^{-\frac{1}{7}} = \frac{1}{x^{\frac{1}{7}}}\)[/tex].
To summarize, the two statements that correctly apply the negative exponent property are:
- [tex]\(17^{-\frac{1}{4}}=\frac{1}{17^{\frac{1}{4}}}\)[/tex]
Thus, the correct answer is:
[tex]\(\bigcirc \, 17^{-\frac{1}{4}}=\frac{1}{17^{\frac{1}{4}}}\)[/tex]
Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thanks for using our service. We're always here to provide accurate and up-to-date answers to all your queries. Get the answers you need at Westonci.ca. Stay informed with our latest expert advice.