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Answer :
To solve this problem, we need to rewrite the expression [tex]\(170 x^4\)[/tex] using radicals. Let's go through the steps:
1. Understand the Expression: The given expression is [tex]\(170 x^4\)[/tex]. Here, [tex]\(x^4\)[/tex] means that you are raising [tex]\(x\)[/tex] to the power of 4.
2. Convert Exponential to Radical Form: In mathematics, a radical expression is another way to write an exponent. Specifically, a power can be expressed as a root.
- The relationship between exponents and radicals is that if you have [tex]\(x^n\)[/tex], it can be rewritten in radical form as [tex]\(\sqrt[n]{x^m}\)[/tex]. In our case, since we have [tex]\(x^4\)[/tex], we can write it as [tex]\(\sqrt[4]{x^4}\)[/tex].
3. Rewriting the Expression: Now that we have identified how to write [tex]\(x^4\)[/tex] as a radical, we incorporate it back into the expression:
- The expression becomes [tex]\(170 \times \sqrt[4]{x^4}\)[/tex].
4. Select the Correct Answer: From the given options, we need to match this expression:
- (A) [tex]\(170 \sqrt[3]{x^4}\)[/tex]
- (B) [tex]\(170 \sqrt[4]{x^5}\)[/tex]
- (C) [tex]\(\sqrt[5]{170 x^4}\)[/tex]
- (D) [tex]\(\sqrt[4]{170 x^5}\)[/tex]
The expression [tex]\(170 \sqrt[4]{x^4}\)[/tex] directly matches option (A), which is written as [tex]\(170 \sqrt[3]{x^4}\)[/tex] in the list. There seems to be a mistake, as this doesn't match the radicals. Let's verify if (B) matches since this seems to be a typographical error on the list.
Upon reconfirming based on understanding the steps, the expression should correctly match the process as [tex]\(170 \times \textrm{power-of }x\)[/tex], resolved correctly in radical context as:
- Your correct answer should have shown [tex]\(170 x^1\)[/tex], direct from understanding [tex]\(\sqrt[4]{x^4}\)[/tex] being self-cancelling on radicals as [tex]\(x\)[/tex].
Please apologize for confusion in process summaries for answer matching.
1. Understand the Expression: The given expression is [tex]\(170 x^4\)[/tex]. Here, [tex]\(x^4\)[/tex] means that you are raising [tex]\(x\)[/tex] to the power of 4.
2. Convert Exponential to Radical Form: In mathematics, a radical expression is another way to write an exponent. Specifically, a power can be expressed as a root.
- The relationship between exponents and radicals is that if you have [tex]\(x^n\)[/tex], it can be rewritten in radical form as [tex]\(\sqrt[n]{x^m}\)[/tex]. In our case, since we have [tex]\(x^4\)[/tex], we can write it as [tex]\(\sqrt[4]{x^4}\)[/tex].
3. Rewriting the Expression: Now that we have identified how to write [tex]\(x^4\)[/tex] as a radical, we incorporate it back into the expression:
- The expression becomes [tex]\(170 \times \sqrt[4]{x^4}\)[/tex].
4. Select the Correct Answer: From the given options, we need to match this expression:
- (A) [tex]\(170 \sqrt[3]{x^4}\)[/tex]
- (B) [tex]\(170 \sqrt[4]{x^5}\)[/tex]
- (C) [tex]\(\sqrt[5]{170 x^4}\)[/tex]
- (D) [tex]\(\sqrt[4]{170 x^5}\)[/tex]
The expression [tex]\(170 \sqrt[4]{x^4}\)[/tex] directly matches option (A), which is written as [tex]\(170 \sqrt[3]{x^4}\)[/tex] in the list. There seems to be a mistake, as this doesn't match the radicals. Let's verify if (B) matches since this seems to be a typographical error on the list.
Upon reconfirming based on understanding the steps, the expression should correctly match the process as [tex]\(170 \times \textrm{power-of }x\)[/tex], resolved correctly in radical context as:
- Your correct answer should have shown [tex]\(170 x^1\)[/tex], direct from understanding [tex]\(\sqrt[4]{x^4}\)[/tex] being self-cancelling on radicals as [tex]\(x\)[/tex].
Please apologize for confusion in process summaries for answer matching.
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