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

Question

Responses

(1/3)^3
left parenthesis Start Fraction 1 over 3 End Fraction right parenthesis cubed

(1/3)^9
left parenthesis Start Fraction 1 over 3 End Fraction right parenthesis superscript 9 baseline

(1/3)^18
left parenthesis Start Fraction 1 over 3 End Fraction right parenthesis superscript 18 baseline

(1/3)^2

Answer 1

Using the Product Rule of Exponents, when you multiply two expressions with the same base, you add their exponents.

In your case, you have:

\[ (1/3)^6 \cdot (1/3)^3 \]

According to the Product Rule:

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

So the equivalent form is:

\[ (1/3)^9 \]

The correct response is:

(1/3)^9