Negative Integer Exponents Practice

Question

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Question
Apply the Property of Negative Integer Exponents to generate an expression equivalent to 7^−3⋅7^−5
with positive exponents only.(1 point)
7^−3⋅7^−5=

Remaining Attempts : 3

Answer 1

To rewrite the expression \(7^{-3} \cdot 7^{-5}\) with positive exponents only, you can use the property of exponents that states:

\[ a^m \cdot a^n = a^{m+n} \]

Applying that property here:

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

Now, to convert \(7^{-8}\) into an expression with positive exponents, you use the property that states:

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

So,

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

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

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