Question

rabbits are not native to australia, so they have no natural predators. oliver wants to compare the number of rabbits that resulted from each rabbit 3 years and 6 years after rabbits were brought into the country. the expression $3^x$ can be used to represent the number of rabbits that resulted from a single rabbit $x$ years after rabbits were brought to australia. determine whether each expression represents the size relationship between of rabbits that resulted from a single rabbit after 6 years and after 3 years. select yes or no for each statement. $\frac{3^6}{3^3}$ yes no $3^2$ yes no $27$ yes no $3^{6div3}$ yes no $3^6 - 3^3$ yes no

Explanation:

Step1: Define target ratio

We need the ratio of rabbits after 6 years to 3 years: $\frac{3^6}{3^3}$

Step2: Simplify the ratio

Use exponent rule $\frac{a^m}{a^n}=a^{m-n}$:
$\frac{3^6}{3^3}=3^{6-3}=3^3=27$

Step3: Evaluate each expression

1. $\frac{3^6}{3^3}$ matches the target: Yes
2. $3^2=9

eq27$: No

1. $27$ matches the simplified value: Yes
2. $3^{6\div3}=3^2=9

eq27$: No

1. $3^6 - 3^3=729-27=702

eq27$: No

Answer:

1. $\frac{3^6}{3^3}$: Yes
2. $3^2$: No
3. $27$: Yes
4. $3^{6\div3}$: No
5. $3^6 - 3^3$: No