To determine which expression is equivalent to \(\frac{r^9}{r^3}\), we can use the properties of exponents. When we divide two expressions that have the same base, we subtract the exponent of the denominator from the exponent of the numerator.
Given the expression \(\frac{r^9}{r^3}\):
1. Identify the base and the exponents:
- The base is \( r \).
- The exponent in the numerator is \( 9 \).
- The exponent in the denominator is \( 3 \).
2. Subtract the exponent in the denominator from the exponent in the numerator:
[tex]\[
\frac{r^9}{r^3} = r^{9-3}
\][/tex]
3. Perform the subtraction:
[tex]\[
9 - 3 = 6
\][/tex]
4. Therefore, the expression simplifies to:
[tex]\[
r^6
\][/tex]
Thus, the expression equivalent to \(\frac{r^9}{r^3}\) is \( r^6 \).
So the correct answer is:
[tex]\[
r^6
\][/tex]
