Let's simplify the expression [tex]\(5^3 \times 5^5\)[/tex].
When multiplying two powers that have the same base, we can use the property of exponents which states [tex]\(a^m \times a^n = a^{m+n}\)[/tex]. Here, the base [tex]\(a\)[/tex] is 5, and we are multiplying [tex]\(5^3\)[/tex] and [tex]\(5^5\)[/tex].
1. Identify the exponents:
- The exponent for the first term [tex]\(5^3\)[/tex] is 3.
- The exponent for the second term [tex]\(5^5\)[/tex] is 5.
2. Add the exponents together:
[tex]\[
3 + 5 = 8
\][/tex]
3. Rewrite the expression using the sum of the exponents:
[tex]\[
5^3 \times 5^5 = 5^{3+5} = 5^8
\][/tex]
4. Calculate the value of [tex]\(5^8\)[/tex]:
[tex]\[
5^8 = 390625
\][/tex]
Now, let's see if the given options match this simplified form:
- A. 52
- B. [tex]\(\frac{1}{6}\)[/tex]
- C. -5
- D. [tex]\(\frac{1}{5^2}\)[/tex]
None of the options given directly correspond to 390625 or [tex]\(5^8\)[/tex]. Hence, it appears none of the provided options (A, B, C, or D) is correct. The correct answer in its simplified form should be [tex]\(5^8\)[/tex], which equals 390625.
