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Answer :
To simplify the expression [tex]\(5^{-8} \times 5^4\)[/tex], we can use the property of exponents that states when multiplying like bases, you add the exponents. This property is [tex]\(a^m \times a^n = a^{m+n}\)[/tex].
Here's how you can simplify the expression step-by-step:
1. Identify the Base and Exponents:
The base is 5, and the exponents are -8 and 4.
2. Apply the Property of Exponents:
[tex]\[
5^{-8} \times 5^4 = 5^{-8 + 4}
\][/tex]
3. Calculate the Sum of the Exponents:
[tex]\[
-8 + 4 = -4
\][/tex]
4. Rewrite the Expression with the New Exponent:
[tex]\[
5^{-4}
\][/tex]
5. Convert the Negative Exponent to a Positive Exponent:
The expression [tex]\(5^{-4}\)[/tex] is the same as [tex]\(\frac{1}{5^4}\)[/tex].
6. Calculate [tex]\(5^4\)[/tex]:
[tex]\[
5^4 = 5 \times 5 \times 5 \times 5 = 625
\][/tex]
7. Final Result:
[tex]\[
5^{-4} = \frac{1}{625}
\][/tex]
Thus, the expression [tex]\(5^{-8} \times 5^4\)[/tex] simplifies to [tex]\(\frac{1}{625}\)[/tex].
Therefore, the correct answer is [tex]\(\boxed{\frac{1}{625}}\)[/tex], which corresponds to option D.
Here's how you can simplify the expression step-by-step:
1. Identify the Base and Exponents:
The base is 5, and the exponents are -8 and 4.
2. Apply the Property of Exponents:
[tex]\[
5^{-8} \times 5^4 = 5^{-8 + 4}
\][/tex]
3. Calculate the Sum of the Exponents:
[tex]\[
-8 + 4 = -4
\][/tex]
4. Rewrite the Expression with the New Exponent:
[tex]\[
5^{-4}
\][/tex]
5. Convert the Negative Exponent to a Positive Exponent:
The expression [tex]\(5^{-4}\)[/tex] is the same as [tex]\(\frac{1}{5^4}\)[/tex].
6. Calculate [tex]\(5^4\)[/tex]:
[tex]\[
5^4 = 5 \times 5 \times 5 \times 5 = 625
\][/tex]
7. Final Result:
[tex]\[
5^{-4} = \frac{1}{625}
\][/tex]
Thus, the expression [tex]\(5^{-8} \times 5^4\)[/tex] simplifies to [tex]\(\frac{1}{625}\)[/tex].
Therefore, the correct answer is [tex]\(\boxed{\frac{1}{625}}\)[/tex], which corresponds to option D.
Thank you for reading the article Simplify the following expression tex 5 8 times 5 4 tex A tex frac 1 390 625 tex B 625 C 390 625 D tex. 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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