Discover answers to your most pressing questions at Westonci.ca, the ultimate Q&A platform that connects you with expert solutions. Get accurate and detailed answers to your questions from a dedicated community of experts on our Q&A platform. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
To determine which of the given expressions is equivalent to [tex]\( -32^{\frac{3}{5}} \)[/tex], we can compare each option to this value.
First, let's evaluate the expression [tex]\( -32^{\frac{3}{5}} \)[/tex]:
1. Option 1: [tex]\(-8\)[/tex]
- We need to determine if [tex]\( \-8 \)[/tex] is equivalent to [tex]\( -32^{\frac{3}{5}} \)[/tex].
2. Option 2: [tex]\(-\sqrt[3]{32^5}\)[/tex]
- This expression can be simplified as follows:
[tex]\[ -\sqrt[3]{32^5} = - ( 32^{5/3} ) \][/tex]
- We need to determine if this value matches with [tex]\(-32^{\frac{3}{5}}\)[/tex].
3. Option 3: [tex]\(\frac{1}{\sqrt[3]{32^5}}\)[/tex]
- This expression can be simplified as follows:
[tex]\[ \frac{1}{\sqrt[3]{32^5}} = \frac{1}{ 32^{5/3} } \][/tex]
- We need to determine if this value matches with [tex]\(-32^{\frac{3}{5}}\)[/tex].
4. Option 4: [tex]\(\frac{1}{8}\)[/tex]
- This expression simplifies as [tex]\(\frac{1}{8}\)[/tex].
- We need to determine if this value matches with [tex]\(-32^{\frac{3}{5}}\)[/tex].
Next, let's look at the numerical results of these comparisons:
- The difference between [tex]\( -32^{\frac{3}{5}} \)[/tex] and [tex]\(-8\)[/tex] is approximately [tex]\(-8.881784197001252e-16\)[/tex]. This value is extremely close to zero, indicating that [tex]\( -32^{\frac{3}{5}} \approx -8 \)[/tex].
- The difference between [tex]\( -32^{\frac{3}{5}} \)[/tex] and [tex]\(-\sqrt[3]{32^5}\)[/tex] is roughly [tex]\(-314.5397887730874\)[/tex]. This large value suggests that [tex]\( -32^{\frac{3}{5}} \)[/tex] is not equivalent to [tex]\(-\sqrt[3]{32^5}\)[/tex].
- The difference between [tex]\( -32^{\frac{3}{5}} \)[/tex] and [tex]\(\frac{1}{\sqrt[3]{32^5}}\)[/tex] is approximately [tex]\(-8.003100392679624\)[/tex]. This indicates they are not the same.
- The difference between [tex]\( -32^{\frac{3}{5}} \)[/tex] and [tex]\(\frac{1}{8}\)[/tex] is approximately 8.125, again indicating they are not the same.
Based on these numerical comparisons, the expression [tex]\( -32^{\frac{3}{5}} \)[/tex] is closest to [tex]\(-8\)[/tex]. Therefore, the correct equivalent expression is:
[tex]\[ -32^{\frac{3}{5}} \approx -8 \][/tex]
Thus, the correct answer is:
[tex]\[ -8 \][/tex]
First, let's evaluate the expression [tex]\( -32^{\frac{3}{5}} \)[/tex]:
1. Option 1: [tex]\(-8\)[/tex]
- We need to determine if [tex]\( \-8 \)[/tex] is equivalent to [tex]\( -32^{\frac{3}{5}} \)[/tex].
2. Option 2: [tex]\(-\sqrt[3]{32^5}\)[/tex]
- This expression can be simplified as follows:
[tex]\[ -\sqrt[3]{32^5} = - ( 32^{5/3} ) \][/tex]
- We need to determine if this value matches with [tex]\(-32^{\frac{3}{5}}\)[/tex].
3. Option 3: [tex]\(\frac{1}{\sqrt[3]{32^5}}\)[/tex]
- This expression can be simplified as follows:
[tex]\[ \frac{1}{\sqrt[3]{32^5}} = \frac{1}{ 32^{5/3} } \][/tex]
- We need to determine if this value matches with [tex]\(-32^{\frac{3}{5}}\)[/tex].
4. Option 4: [tex]\(\frac{1}{8}\)[/tex]
- This expression simplifies as [tex]\(\frac{1}{8}\)[/tex].
- We need to determine if this value matches with [tex]\(-32^{\frac{3}{5}}\)[/tex].
Next, let's look at the numerical results of these comparisons:
- The difference between [tex]\( -32^{\frac{3}{5}} \)[/tex] and [tex]\(-8\)[/tex] is approximately [tex]\(-8.881784197001252e-16\)[/tex]. This value is extremely close to zero, indicating that [tex]\( -32^{\frac{3}{5}} \approx -8 \)[/tex].
- The difference between [tex]\( -32^{\frac{3}{5}} \)[/tex] and [tex]\(-\sqrt[3]{32^5}\)[/tex] is roughly [tex]\(-314.5397887730874\)[/tex]. This large value suggests that [tex]\( -32^{\frac{3}{5}} \)[/tex] is not equivalent to [tex]\(-\sqrt[3]{32^5}\)[/tex].
- The difference between [tex]\( -32^{\frac{3}{5}} \)[/tex] and [tex]\(\frac{1}{\sqrt[3]{32^5}}\)[/tex] is approximately [tex]\(-8.003100392679624\)[/tex]. This indicates they are not the same.
- The difference between [tex]\( -32^{\frac{3}{5}} \)[/tex] and [tex]\(\frac{1}{8}\)[/tex] is approximately 8.125, again indicating they are not the same.
Based on these numerical comparisons, the expression [tex]\( -32^{\frac{3}{5}} \)[/tex] is closest to [tex]\(-8\)[/tex]. Therefore, the correct equivalent expression is:
[tex]\[ -32^{\frac{3}{5}} \approx -8 \][/tex]
Thus, the correct answer is:
[tex]\[ -8 \][/tex]
Thanks for stopping by. We are committed to providing the best answers for all your questions. See you again soon. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.
