Answer:
[tex]\frac{1}{27}[/tex]
Step-by-step explanation:
3^2 ⋅ 3^−5
[tex]3^2 \cdot 3^{-5}[/tex]
To multiply the exponents we apply exponential property
[tex]a^m \cdot a^n = a^{m+n}[/tex]
When we multiply the exponents with same base then we add the exponents
[tex]3^2 \cdot 3^{-5}[/tex], both terms has same base . so we add the exponents.
[tex]3^2 \cdot 3^{-5}=3^{2-5}= 3^{-3}[/tex]
Now we make the exponent positive
[tex]a^{-m}= \frac{1}{a^m}[/tex]
[tex]3^{-3}= \frac{1}{3^3}=\frac{1}{27}[/tex]
