se the Product Rule of Exponents to simplify 3 to the5 power⋅3to the7 power Show your work. (1 point) Responses 935 9 to the 35th power 335 3 to the 35th power 312 3 to the 12th power 912

Answer 1

To simplify $3^5\cdot 3^7$ using the Product Rule of Exponents, we can combine the exponents since the bases are the same.

The Product Rule states that when multiplying two exponential expressions with the same base, you add the exponents:

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

In this case, our base $a$ is $3$, $m$ is $5$, and $n$ is $7$. So we add the exponents:

$$3^5\cdot 3^7=3^{5+7}=3^{12}$$

Thus, $3^5\cdot 3^7$ simplifies to $3^{12}$.

The correct response is:

3 to the 12th power (312).