Question
If the expression 5^10 was simplified using the Power Rule of Exponents, what would be the expanded equivalent expression? Show your work.
Answers
GPT-4o mini
The Power Rule of Exponents states that if you have a number raised to a power and you want to express it in terms of multiplication, you need to understand that the expression \( a^n \) can be expanded as multiplying the base \( a \) by itself \( n \) times.
For the expression \( 5^{10} \):
Using the Power Rule:
\[
5^{10} = 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5
\]
This means that \( 5^{10} \) is the same as multiplying the number 5 by itself a total of 10 times.
In summary, the expanded equivalent expression of \( 5^{10} \) is:
\[
5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5
\]
For the expression \( 5^{10} \):
Using the Power Rule:
\[
5^{10} = 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5
\]
This means that \( 5^{10} \) is the same as multiplying the number 5 by itself a total of 10 times.
In summary, the expanded equivalent expression of \( 5^{10} \) is:
\[
5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5
\]