Connect with a community that values knowledge and expertise on IDNLearn.com. Ask any question and receive accurate, in-depth responses from our dedicated team of experts.
Sagot :
To determine which of the given expressions are equivalent to [tex]\( x^{9/4} \)[/tex], we need to see if we can rewrite each expression to match [tex]\( x^{9/4} \)[/tex].
Let's analyze each expression step-by-step:
Expression A: [tex]\(\left(x^4\right)^{1 / 9}\)[/tex]
- Rewriting this expression using the power of a power rule [tex]\((a^m)^n = a^{mn}\)[/tex], we get:
[tex]\[ \left(x^4\right)^{1 / 9} = x^{4 \cdot (1 / 9)} = x^{4/9} \][/tex]
This is not equivalent to [tex]\( x^{9/4} \)[/tex].
Expression B: [tex]\((\sqrt[4]{x})^9\)[/tex]
- Rewriting [tex]\(\sqrt[4]{x}\)[/tex] as [tex]\( x^{1/4} \)[/tex], we get:
[tex]\[ (\sqrt[4]{x})^9 = (x^{1/4})^9 = x^{(1/4) \cdot 9} = x^{9/4} \][/tex]
This is equivalent to [tex]\( x^{9/4} \)[/tex].
Expression C: [tex]\(\sqrt[9]{x^4}\)[/tex]
- Rewriting [tex]\(\sqrt[9]{x^4}\)[/tex] as [tex]\( (x^4)^{1/9} \)[/tex], we get:
[tex]\[ \sqrt[9]{x^4}= (x^4)^{1/9} = x^{4 \cdot (1/9)} = x^{4/9} \][/tex]
This is not equivalent to [tex]\( x^{9/4} \)[/tex].
Expression D: [tex]\(\sqrt[4]{x^9}\)[/tex]
- Rewriting [tex]\(\sqrt[4]{x^9}\)[/tex] as [tex]\( (x^9)^{1/4} \)[/tex], we get:
[tex]\[ \sqrt[4]{x^9} = (x^9)^{1/4} = x^{9 \cdot (1/4)} = x^{9/4} \][/tex]
This is equivalent to [tex]\( x^{9/4} \)[/tex].
Expression E: [tex]\((x^9)^{1 / 4}\)[/tex]
- Rewriting [tex]\((x^9)^{1 / 4}\)[/tex] using the power of a power rule, we get:
[tex]\[ (x^9)^{1/4} = x^{9 \cdot (1/4)} = x^{9/4} \][/tex]
This is equivalent to [tex]\( x^{9/4} \)[/tex].
Expression F: [tex]\((\sqrt[3]{x})^4\)[/tex]
- Rewriting [tex]\(\sqrt[3]{x}\)[/tex] as [tex]\( x^{1/3} \)[/tex], we get:
[tex]\[ (\sqrt[3]{x})^4 = (x^{1/3})^4 = x^{(1/3) \cdot 4} = x^{4/3} \][/tex]
This is not equivalent to [tex]\( x^{9/4} \)[/tex].
So, the expressions that are equivalent to [tex]\( x^{9/4} \)[/tex] are:
- Expression B: [tex]\((\sqrt[4]{x})^9\)[/tex]
- Expression D: [tex]\(\sqrt[4]{x^9}\)[/tex]
- Expression E: [tex]\((x^9)^{1 / 4}\)[/tex]
Therefore, the correct answers are B, D, and E.
Let's analyze each expression step-by-step:
Expression A: [tex]\(\left(x^4\right)^{1 / 9}\)[/tex]
- Rewriting this expression using the power of a power rule [tex]\((a^m)^n = a^{mn}\)[/tex], we get:
[tex]\[ \left(x^4\right)^{1 / 9} = x^{4 \cdot (1 / 9)} = x^{4/9} \][/tex]
This is not equivalent to [tex]\( x^{9/4} \)[/tex].
Expression B: [tex]\((\sqrt[4]{x})^9\)[/tex]
- Rewriting [tex]\(\sqrt[4]{x}\)[/tex] as [tex]\( x^{1/4} \)[/tex], we get:
[tex]\[ (\sqrt[4]{x})^9 = (x^{1/4})^9 = x^{(1/4) \cdot 9} = x^{9/4} \][/tex]
This is equivalent to [tex]\( x^{9/4} \)[/tex].
Expression C: [tex]\(\sqrt[9]{x^4}\)[/tex]
- Rewriting [tex]\(\sqrt[9]{x^4}\)[/tex] as [tex]\( (x^4)^{1/9} \)[/tex], we get:
[tex]\[ \sqrt[9]{x^4}= (x^4)^{1/9} = x^{4 \cdot (1/9)} = x^{4/9} \][/tex]
This is not equivalent to [tex]\( x^{9/4} \)[/tex].
Expression D: [tex]\(\sqrt[4]{x^9}\)[/tex]
- Rewriting [tex]\(\sqrt[4]{x^9}\)[/tex] as [tex]\( (x^9)^{1/4} \)[/tex], we get:
[tex]\[ \sqrt[4]{x^9} = (x^9)^{1/4} = x^{9 \cdot (1/4)} = x^{9/4} \][/tex]
This is equivalent to [tex]\( x^{9/4} \)[/tex].
Expression E: [tex]\((x^9)^{1 / 4}\)[/tex]
- Rewriting [tex]\((x^9)^{1 / 4}\)[/tex] using the power of a power rule, we get:
[tex]\[ (x^9)^{1/4} = x^{9 \cdot (1/4)} = x^{9/4} \][/tex]
This is equivalent to [tex]\( x^{9/4} \)[/tex].
Expression F: [tex]\((\sqrt[3]{x})^4\)[/tex]
- Rewriting [tex]\(\sqrt[3]{x}\)[/tex] as [tex]\( x^{1/3} \)[/tex], we get:
[tex]\[ (\sqrt[3]{x})^4 = (x^{1/3})^4 = x^{(1/3) \cdot 4} = x^{4/3} \][/tex]
This is not equivalent to [tex]\( x^{9/4} \)[/tex].
So, the expressions that are equivalent to [tex]\( x^{9/4} \)[/tex] are:
- Expression B: [tex]\((\sqrt[4]{x})^9\)[/tex]
- Expression D: [tex]\(\sqrt[4]{x^9}\)[/tex]
- Expression E: [tex]\((x^9)^{1 / 4}\)[/tex]
Therefore, the correct answers are B, D, and E.
B and D and E
B = (c^1/4)^9 = x^9/4
D = (x^9*1/4) = x^9/4
E = (x^9)^1/4 = x^9/4
B = (c^1/4)^9 = x^9/4
D = (x^9*1/4) = x^9/4
E = (x^9)^1/4 = x^9/4
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.
