Answered

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Use the Product Rule of Exponents to simplify [tex]$5^{10} \cdot 5^5$[/tex].

A. [tex]$25^{15}$[/tex]
B. [tex]$5^{50}$[/tex]
C. [tex]$5^{15}$[/tex]
D. [tex]$25^{50}$[/tex]

Sagot :

GinnyAnswer
To simplify \(5^{10} \cdot 5^5\) using the Product Rule of Exponents, please follow these steps:

1. Identify the base and the exponents:
- Here, the base is 5.
- The exponents are 10 and 5 respectively.

2. Apply the Product Rule of Exponents:
- The Product Rule of Exponents states that \(a^m \cdot a^n = a^{m+n}\), where \(a\) is the base and \(m\) and \(n\) are the exponents.
- In this case, we have \(5^{10} \cdot 5^5\).

3. Combine the exponents:
- According to the rule, add the exponents together: \(10 + 5\).
- This gives us \(5^{10+5} = 5^{15}\).

So, the simplified expression is \(5^{15}\).

Among the given options, the correct simplified expression is:
[tex]\[ 5^{15} \][/tex]

Thus, the correct answer is:
[tex]\[ 5^{15} \][/tex]
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