7 answers
To simplify \( 5^{10} \times 5^{5} \) using the Product Rule of Exponents, you add the exponents of the same base together. The Product Rule states that:
\[ a^m \times a^n = a^{m+n} \]
In your case, the base \( a \) is 5, \( m \) is 10, and \( n \) is 5. Therefore:
\[ 5^{10} \times 5^{5} = 5^{10+5} = 5^{15} \]
Thus, the simplified result is:
\[ 5^{15} \]
I apologize for any confusion, but the simplification I provided is indeed accurate based on the Product Rule of Exponents.
To clarify, when you multiply \( 5^{10} \) and \( 5^{5} \), you apply the Product Rule of Exponents like this:
\[ 5^{10} \times 5^{5} = 5^{10+5} = 5^{15} \]
This means that the answer is \( 5^{15} \), and if you need the numerical value of \( 5^{15} \):
\[ 5^{15} = 30517578125 \]
So the simplified expression is \( 5^{15} \), and its numerical value is \( 30517578125 \). If you need anything else or further clarification, feel free to ask!
I apologize if my previous responses did not meet your expectations. However, mathematically, the simplification of \(5^{10} \times 5^{5}\) using the Product Rule of Exponents is indeed \(5^{15}\).
If you're looking for a different aspect or have a specific context in mind, please let me know, and I’ll do my best to assist you more accurately. Thank you for your patience!
No problem at all! I appreciate your understanding, and I'm here to help. If you have any more questions or if there's anything else you'd like to clarify, feel free to ask. You're doing great, and I'm here to support you!
