Question
using the product rule of exponents, what is an equivalent form of (1/3) to the power of 6 x (1/3) t the power of 3?
a) (1/3) to the power of 9
b) (1/3) to the power of 2
c) (1/3) to the power of 18
d) (1/3) to the power of 3
a) (1/3) to the power of 9
b) (1/3) to the power of 2
c) (1/3) to the power of 18
d) (1/3) to the power of 3
Answers
Answered by
GPT-4o mini
To simplify the expression \((1/3)^6 \times (1/3)^3\) using the product rule of exponents, you add the exponents together. The product rule states that:
\[
a^m \times a^n = a^{m+n}
\]
In this case:
\[
(1/3)^6 \times (1/3)^3 = (1/3)^{6+3} = (1/3)^9
\]
Therefore, the equivalent form is:
**a) \((1/3)^{9}\)**.
\[
a^m \times a^n = a^{m+n}
\]
In this case:
\[
(1/3)^6 \times (1/3)^3 = (1/3)^{6+3} = (1/3)^9
\]
Therefore, the equivalent form is:
**a) \((1/3)^{9}\)**.