Powers: Basic Rules - Raising a Power to Another Power

Which of the following has the same value as $$3^9$$?

Correct. [[Snippet]] Notice that $$27^3 = (3^3)^3 = 3^{3\cdot3} = 3^9$$. Since $$27^3$$ is the only answer choice equal in value to $$3^9$$, this is the correct answer.

Incorrect. [[Snippet]] Notice that $$9^3 = (3^2)^3 = 3^{2 \cdot 3} = 3^6$$. Hence, eliminate this answer choice.

Incorrect. [[Snippet]] Notice that $$81 = 9^2 = (3^2)^2 = 3^{2 \cdot 2} = 3^4$$. Hence, eliminate this answer choice.

Incorrect. [[Snippet]] Notice that $$81^2 = (9^2)^2 = 9^{2 \cdot 2} = 9^4 = (3^2)^4 = 3^{2 \cdot 4} = 3^8$$. Hence, eliminate this answer choice.

Incorrect. [[Snippet]] Notice that $$243 = 9 \cdot 27 = 3^2 \cdot 3^3 = 3^5$$. Hence, eliminate this answer choice.

$$81$$

$$9^3$$

$$27^3$$

$$81^2$$

$$243$$