Apply All Exponent Rules Practice Complete this assessment to review what you've learned. It will not count toward your grade. 1 of 51 of 5 Items Question Apply the Properties of Integer Exponents to generate equivalent expressions to 3^7⋅3^−9 with only positive exponents, then solve the expression. Your answer will be a simplified fraction with no remaining exponents.(1 point) 3^7⋅3^−9= Remaining Attempts : 3 Skip to navigation

Answer 1

To solve the expression \( 3^7 \cdot 3^{-9} \) using the properties of exponents, we can apply the rule that states:

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

Applying this rule to our expression:

\[ 3^7 \cdot 3^{-9} = 3^{7 + (-9)} = 3^{-2} \]

Next, we can convert \( 3^{-2} \) to have a positive exponent by using the property of exponents that states:

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

Thus:

\[ 3^{-2} = \frac{1}{3^2} \]

Now we can evaluate \( 3^2 \):

\[ 3^2 = 9 \]

So we have:

\[ 3^{-2} = \frac{1}{9} \]

Therefore, the equivalent expression with only positive exponents is:

\[ 3^7 \cdot 3^{-9} = \frac{1}{9} \]

Final answer: \( \frac{1}{9} \)