Question
Which of the following correctly used the Product Rule of Exponents to simplify the expression 1008 -100'?
Answers
GPT-4o mini
To simplify the expression \( 1008 - 100' \) using the Product Rule of Exponents, we first need to clarify the expression. It looks like there might be a typographical or formatting error in "100'". I assume you meant \( 10^0 \) (which equals 1) or potentially another exponent.
If we take the expression as \( 100^8 - 100^1 \):
Using the Product Rule of Exponents, the expression can indeed be simplified. According to the Product Rule of Exponents,
\[ a^m - a^n = a^n (a^{m-n} - 1) \]
for \( a = 100 \), \( m = 8 \), and \( n = 1 \).
Using this rule, we can rewrite the expression:
\[
= 100^1 (100^{8-1} - 1)
\]
\[
= 100 (100^7 - 1)
\]
This is the correct application of the Product Rule of Exponents to the expression \( 100^8 - 100^1 \).
If the expression you wanted to evaluate was different, please provide the correct terms so I can assist you more accurately!
If we take the expression as \( 100^8 - 100^1 \):
Using the Product Rule of Exponents, the expression can indeed be simplified. According to the Product Rule of Exponents,
\[ a^m - a^n = a^n (a^{m-n} - 1) \]
for \( a = 100 \), \( m = 8 \), and \( n = 1 \).
Using this rule, we can rewrite the expression:
\[
= 100^1 (100^{8-1} - 1)
\]
\[
= 100 (100^7 - 1)
\]
This is the correct application of the Product Rule of Exponents to the expression \( 100^8 - 100^1 \).
If the expression you wanted to evaluate was different, please provide the correct terms so I can assist you more accurately!