Question

Use the properties of rational exponents to EVALUATE: (8¹/³))*25¹/²))³

Answer 1

To evaluate the expression (8¹/³) * (25¹/²))³, we find the cube root of 8 which is 2, the square root of 25 which is 5, multiply them to get 10, and then cube 10 to get 1000 as the final answer.

Step-by-step explanation:

To evaluate the expression ((8¹/³) * (25¹/²))³, using the properties of rational exponents, we follow several steps.

First, we simplify inside the parentheses:

• 8¹/³ is the cube root of 8, which is 2, because 2³ = 8.
• 25¹/² is the square root of 25, which is 5, because 5² = 25.

The expression inside the parentheses simplifies to (2 * 5).

We then evaluate:

• (2 * 5) = 10
• 10³ = 10 * 10 * 10

Thus, 10³ equals 1000.

The final answer is 1000.