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Answer :
To simplify the expression [tex]\(5^{-8} \times 5^4\)[/tex], we can use the properties of exponents. Here are the steps:
1. Use the Product of Powers Property: The property states that when multiplying two powers with the same base, you add the exponents. So for [tex]\(5^{-8} \times 5^4\)[/tex], we combine the exponents:
[tex]\[
5^{-8 + 4} = 5^{-4}
\][/tex]
2. Negative Exponent Rule: A negative exponent means that the base is on the wrong side of the fraction line, so you take the reciprocal of the base and make the exponent positive:
[tex]\[
5^{-4} = \frac{1}{5^4}
\][/tex]
3. Calculate [tex]\(5^4\)[/tex]:
[tex]\[
5^4 = 5 \times 5 \times 5 \times 5 = 625
\][/tex]
4. Write the Final Answer:
[tex]\[
\frac{1}{5^4} = \frac{1}{625}
\][/tex]
So, the simplified expression is [tex]\(\frac{1}{625}\)[/tex].
Therefore, the correct answer is option A: [tex]\(\frac{1}{625}\)[/tex].
1. Use the Product of Powers Property: The property states that when multiplying two powers with the same base, you add the exponents. So for [tex]\(5^{-8} \times 5^4\)[/tex], we combine the exponents:
[tex]\[
5^{-8 + 4} = 5^{-4}
\][/tex]
2. Negative Exponent Rule: A negative exponent means that the base is on the wrong side of the fraction line, so you take the reciprocal of the base and make the exponent positive:
[tex]\[
5^{-4} = \frac{1}{5^4}
\][/tex]
3. Calculate [tex]\(5^4\)[/tex]:
[tex]\[
5^4 = 5 \times 5 \times 5 \times 5 = 625
\][/tex]
4. Write the Final Answer:
[tex]\[
\frac{1}{5^4} = \frac{1}{625}
\][/tex]
So, the simplified expression is [tex]\(\frac{1}{625}\)[/tex].
Therefore, 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 tex frac 1 390 625 tex C. 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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