Apply the Property of Negative Integer Exponents to generate an expression equivalent to 7(−3) ⋅ 7(−5)

Question

with positive exponents only.(1 point)

Answer 1

To apply the property of negative integer exponents, we can use the fact that \( a^{-n} = \frac{1}{a^n} \) to convert the exponents into positive ones.

Starting with the expression:

\[ 7^{-3} \cdot 7^{-5} \]

We can combine the terms using the property of exponents \( a^m \cdot a^n = a^{m+n} \):

\[ 7^{-3} \cdot 7^{-5} = 7^{-3 + (-5)} = 7^{-8} \]

Now, we can convert the negative exponent to a positive exponent:

\[ 7^{-8} = \frac{1}{7^8} \]

So the expression \( 7^{-3} \cdot 7^{-5} \) with positive exponents only is:

\[ \frac{1}{7^8} \]