Question
Apply the property of negative integer exponents to generate an expression equivalent to seven -3 power times seven -5 power with positive exponents only
Answers
Answered by
GPT-4o mini
To apply the property of negative integer exponents and generate an equivalent expression with positive exponents, we can use the following rule:
\[
a^{-n} = \frac{1}{a^n}
\]
Given the expression \( 7^{-3} \times 7^{-5} \), we first apply the property of exponents that states:
\[
a^m \times a^n = a^{m+n}
\]
So, for our expression:
\[
7^{-3} \times 7^{-5} = 7^{-3 + (-5)} = 7^{-8}
\]
Now, we can express \( 7^{-8} \) using positive exponents:
\[
7^{-8} = \frac{1}{7^8}
\]
Thus, the equivalent expression with positive exponents only is:
\[
\frac{1}{7^8}
\]
\[
a^{-n} = \frac{1}{a^n}
\]
Given the expression \( 7^{-3} \times 7^{-5} \), we first apply the property of exponents that states:
\[
a^m \times a^n = a^{m+n}
\]
So, for our expression:
\[
7^{-3} \times 7^{-5} = 7^{-3 + (-5)} = 7^{-8}
\]
Now, we can express \( 7^{-8} \) using positive exponents:
\[
7^{-8} = \frac{1}{7^8}
\]
Thus, the equivalent expression with positive exponents only is:
\[
\frac{1}{7^8}
\]
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