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?

Question

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

Answer 1

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) \((1/3)^{9}\).