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

Question

with positive exponents only.(1 point)
7^−3⋅7^−5=

Answer 1

To simplify the expression \( 7^{-3} \cdot 7^{-5} \) using the properties of exponents, we can apply the rule that states \( a^m \cdot a^n = a^{m+n} \).

In this case, we have:

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

To express \( 7^{-8} \) with positive exponents, we use the property that \( a^{-n} = \frac{1}{a^n} \):

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

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

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