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Answer :
To simplify the expression [tex]\( 5^{-8} \times 5^4 \)[/tex], we can use the exponent rule which states that when multiplying powers with the same base, you add the exponents. Here's how you can simplify it step by step:
1. Identify the Base and Exponents:
- The base here is 5 for both terms.
- The exponents are [tex]\(-8\)[/tex] and [tex]\(4\)[/tex].
2. Apply the Exponent Rule:
- When you multiply terms with the same base, you add the exponents: [tex]\( a^m \times a^n = a^{m+n} \)[/tex].
- So, [tex]\( 5^{-8} \times 5^4 = 5^{-8 + 4} \)[/tex].
3. Compute the New Exponent:
- [tex]\(-8 + 4 = -4\)[/tex].
- This means we now have [tex]\( 5^{-4} \)[/tex].
4. Interpret the Negative Exponent:
- A negative exponent means we take the reciprocal of the base raised to the positive of that exponent: [tex]\( a^{-n} = \frac{1}{a^n} \)[/tex].
- Therefore, [tex]\( 5^{-4} = \frac{1}{5^4} \)[/tex].
5. Calculate [tex]\(5^4\)[/tex]:
- [tex]\( 5^4 = 5 \times 5 \times 5 \times 5 = 625 \)[/tex].
6. Find the Final Result:
- Substituting this back into the expression, [tex]\( 5^{-4} = \frac{1}{625} \)[/tex].
So the simplified result of the expression [tex]\( 5^{-8} \times 5^4 \)[/tex] is [tex]\( \frac{1}{625} \)[/tex].
Therefore, the correct choice is C. [tex]\(\frac{1}{625}\)[/tex].
1. Identify the Base and Exponents:
- The base here is 5 for both terms.
- The exponents are [tex]\(-8\)[/tex] and [tex]\(4\)[/tex].
2. Apply the Exponent Rule:
- When you multiply terms with the same base, you add the exponents: [tex]\( a^m \times a^n = a^{m+n} \)[/tex].
- So, [tex]\( 5^{-8} \times 5^4 = 5^{-8 + 4} \)[/tex].
3. Compute the New Exponent:
- [tex]\(-8 + 4 = -4\)[/tex].
- This means we now have [tex]\( 5^{-4} \)[/tex].
4. Interpret the Negative Exponent:
- A negative exponent means we take the reciprocal of the base raised to the positive of that exponent: [tex]\( a^{-n} = \frac{1}{a^n} \)[/tex].
- Therefore, [tex]\( 5^{-4} = \frac{1}{5^4} \)[/tex].
5. Calculate [tex]\(5^4\)[/tex]:
- [tex]\( 5^4 = 5 \times 5 \times 5 \times 5 = 625 \)[/tex].
6. Find the Final Result:
- Substituting this back into the expression, [tex]\( 5^{-4} = \frac{1}{625} \)[/tex].
So the simplified result of the expression [tex]\( 5^{-8} \times 5^4 \)[/tex] is [tex]\( \frac{1}{625} \)[/tex].
Therefore, the correct choice is C. [tex]\(\frac{1}{625}\)[/tex].
Thank you for reading the article Simplify the following expression tex 5 8 times 5 4 tex A 390 625 B 625 C tex frac 1 625 tex D tex frac. 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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