Question

Which expression is equivalent to 3^2 ⋅ 3^−5?

Answer 1

The answer to 3^2 ⋅ 3^−5 is 1/27=.037

The answer is 1/27

Answer 2

Answer:

$\frac{1}{27}$

Step-by-step explanation:

3^2 ⋅ 3^−5

$3^2 \cdot 3^{-5}$

To multiply the exponents we apply exponential property

$a^m \cdot a^n = a^{m+n}$

When we multiply the exponents with same base then we add the exponents

$3^2 \cdot 3^{-5}$, both terms has same base . so we add the exponents.

$3^2 \cdot 3^{-5}=3^{2-5}= 3^{-3}$

Now we make the exponent positive

$a^{-m}= \frac{1}{a^m}$

$3^{-3}= \frac{1}{3^3}=\frac{1}{27}$