Griffiths Guzman
04/29/2023 · Middle School
Apply the Property of Negative Integer Exponents to generate an expression equivalent to \( 7^{-3} \cdot 7^{-5} \) with positive exponents only. (1 point) \( 7^{-3} \cdot 7^{-5}= \) Check answer Remaining Attempts : 3
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Step-by-step Solution
To apply the property of negative integer exponents, we can use the rule that states:
\[
a^{-n} = \frac{1}{a^n}
\]
First, we can combine the exponents of the same base using the property of exponents:
\[
7^{-3} \cdot 7^{-5} = 7^{-3 + (-5)} = 7^{-8}
\]
Now, we can convert \( 7^{-8} \) to an expression with positive exponents:
\[
7^{-8} = \frac{1}{7^8}
\]
Thus, the expression equivalent to \( 7^{-3} \cdot 7^{-5} \) with positive exponents only is:
\[
\frac{1}{7^8}
\]
Quick Answer
\( 7^{-3} \cdot 7^{-5} = \frac{1}{7^8} \)
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