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

`(1)/(27)`

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)= (1)/(a^m)`

`3^(-3)= (1)/(3^3)=(1)/(27)`