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 \( 7^{-3} \cdot 7^{-5} \) using the property of negative integer exponents, we can first use the property:

\[ a^{-n} = \frac{1}{a^n} \]

Applying this property, we have:

\[ 7^{-3} \cdot 7^{-5} = \frac{1}{7^3} \cdot \frac{1}{7^5} \]

Now, we can combine the fractions:

\[ \frac{1}{7^3} \cdot \frac{1}{7^5} = \frac{1}{7^{3+5}} = \frac{1}{7^8} \]

Thus, the expression \( 7^{-3} \cdot 7^{-5} \) can be expressed with positive exponents as:

\[ 7^{-3} \cdot 7^{-5} = \frac{1}{7^8} \]