Question
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
Answers
GPT-4o mini
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: \( \frac{1}{9} \)
\[
a^m \cdot a^n = a^{m+n}
\]
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: \( \frac{1}{9} \)