How to Simplify 125^(2/3) for 11-Year-Old Students

Let's simplify the expression 125^(2/3) step by step.

When you see something like a raised to a fraction, like a^(m/n), it means:

1. Take the nth root of a. (That's the root in the denominator.)
2. Then raise the result to the mth power. (That's the numerator.)

So for 125^(2/3):

• The denominator is 3, so we find the cube root (third root) of 125.
• The numerator is 2, so we square (raise to power 2) the result.

Step 1: Find the cube root of 125.

Cube root of 125 means a number which when multiplied by itself 3 times equals 125.

Since 5 x 5 x 5 = 125, the cube root of 125 is 5.

Step 2: Now, raise 5 to the power 2.

5^2 = 5 x 5 = 25.

Therefore, 125^(2/3) = 25.

Summary: 125^(2/3) = (cube root of 125)^2 = 5^2 = 25.