Using the Product Rule of Exponents, what is an equivalent form of (1/3)^6⋅(1/3)^3 ?

Answer 1

To simplify the expression $(1/3{)}^6\cdot (1/3{)}^3$ using the Product Rule of Exponents, we can use the rule that states:

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

In this case, $a=\frac{1}{3}$, $m=6$, and $n=3$. Applying the rule:

$$(1/3{)}^6\cdot (1/3{)}^3=(1/3{)}^{6+3}=(1/3{)}^9$$

Thus, an equivalent form of the expression $(1/3{)}^6\cdot (1/3{)}^3$ is:

$$\boxed{{\displaystyle (1/3{)}^9}}$$