Question

What is the ratio of \( \left( \frac{1}{3} \right)^2 \) to \( \left( \frac{1}{3} \right)^4 \)?

• A. 9
• B. 3
• C. 1
• D. 1:3
• E. 1:27

Hint:

When dividing powers with the same base, subtract the exponents.

Answer 1

Answer: (E)

Step 1: Write the ratio of the powers.
We are asked to find the ratio of \( \left( \frac{1}{3} \right)^2 \) to \( \left( \frac{1}{3} \right)^4 \). We can write the ratio as: \[ \frac{\left( \frac{1}{3} \right)^2}{\left( \frac{1}{3} \right)^4} = \left( \frac{1}{3} \right)^{2 - 4} = \left( \frac{1}{3} \right)^{-2}. \] Step 2: Simplify the expression.
We know that \( \left( \frac{1}{3} \right)^{-2} = 3^2 = 9 \). Hence, the ratio is: \[ 9. \] Step 3: Conclusion.
The correct answer is (E) 1:27.