Question

Evaluate \( (0.2)^{\frac{1}{3}} \) to \( (0.2)^{\frac{5}{3}} \).

• A. 0.0008
• B. 0.001
• C. 0.008
• D. 0.04
• E. 0.08

Hint:

When multiplying powers of the same base, add the exponents.

Answer 1

The Correct Option is C

Step 1: Express the terms as powers of 0.2.
We are asked to evaluate the expression \( (0.2)^{\frac{1}{3}} \times (0.2)^{\frac{5}{3}} \). Using the properties of exponents: \[ (0.2)^{\frac{1}{3}} \times (0.2)^{\frac{5}{3}} = (0.2)^{\frac{1}{3} + \frac{5}{3}} = (0.2)^2. \] Step 2: Simplify the expression.
Now, we evaluate \( (0.2)^2 \): \[ (0.2)^2 = 0.04. \] Step 3: Conclusion.
The correct answer is (C) 0.008.