Question

Use radical notation to write 8^(2/3).

Answer 1

The expression 8^(2/3) is written in radical notation as √(8^2), which simplifies to the cube root of 64. This denotes that 8 should be squared to get 64, and then the number 64 should be taken to the cube root.

Step-by-step explanation:

To use radical notation to write 8^(2/3), recognize that the fractional exponent can be broken into two parts: the numerator (2) indicates the power to which the number is to be raised, and the denominator (3) indicates the root to be taken. In this case, 8 is to be squared and then the cube root is to be taken. Therefore, in radical notation, this expression is written as √(8^2), since the cube root of a number is denoted by a radical sign with an index of 3 (which is often omitted when written by hand or in print, as the cube root is assumed).

Here's the step-by-step conversion:

1. Write the number 8.
2. Square the number 8 to get 64.
3. Write the cube root symbol, which is a radical with an index of 3 (or just the radical sign for shorthand).
4. Combine the radical sign and 64 to get the final radical notation √64.

So, in radical notation, the expression 8^(2/3) is equivalent to √64 or the cube root of 64.