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Answer :
To simplify the expression [tex]\(5^{-8} \times 5^4\)[/tex], we can use the property of exponents:
[tex]\[
a^m \times a^n = a^{m+n}
\][/tex]
Here's a step-by-step solution:
1. Identify the base and exponents:
- The base is [tex]\(5\)[/tex].
- The exponents are [tex]\(-8\)[/tex] and [tex]\(4\)[/tex].
2. Apply the property of exponents:
- Combine the exponents by adding them: [tex]\(-8 + 4 = -4\)[/tex].
3. Rewrite the expression:
- The expression [tex]\(5^{-8} \times 5^4\)[/tex] simplifies to [tex]\(5^{-4}\)[/tex].
4. Express using positive exponents:
- Recall that [tex]\(a^{-n} = \frac{1}{a^n}\)[/tex]. This means [tex]\(5^{-4} = \frac{1}{5^4}\)[/tex].
5. Calculate [tex]\(5^4\)[/tex]:
- Find [tex]\(5^4 = 5 \times 5 \times 5 \times 5 = 625\)[/tex].
6. Write the final answer:
- So, [tex]\(5^{-4} = \frac{1}{625}\)[/tex].
Therefore, the simplified expression is [tex]\(\frac{1}{625}\)[/tex]. The correct answer is option A. [tex]\(\frac{1}{625}\)[/tex].
[tex]\[
a^m \times a^n = a^{m+n}
\][/tex]
Here's a step-by-step solution:
1. Identify the base and exponents:
- The base is [tex]\(5\)[/tex].
- The exponents are [tex]\(-8\)[/tex] and [tex]\(4\)[/tex].
2. Apply the property of exponents:
- Combine the exponents by adding them: [tex]\(-8 + 4 = -4\)[/tex].
3. Rewrite the expression:
- The expression [tex]\(5^{-8} \times 5^4\)[/tex] simplifies to [tex]\(5^{-4}\)[/tex].
4. Express using positive exponents:
- Recall that [tex]\(a^{-n} = \frac{1}{a^n}\)[/tex]. This means [tex]\(5^{-4} = \frac{1}{5^4}\)[/tex].
5. Calculate [tex]\(5^4\)[/tex]:
- Find [tex]\(5^4 = 5 \times 5 \times 5 \times 5 = 625\)[/tex].
6. Write the final answer:
- So, [tex]\(5^{-4} = \frac{1}{625}\)[/tex].
Therefore, the simplified expression is [tex]\(\frac{1}{625}\)[/tex]. The correct answer is option A. [tex]\(\frac{1}{625}\)[/tex].
Thank you for reading the article Simplify the following expression tex 5 8 times 5 4 tex A tex frac 1 625 tex B 625 C tex frac 1 390 625. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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