Rewrite the radical as a rational exponent: the cube root of 2 to the seventh power

To rewrite the cube root of 2 to the seventh power as a rational exponent, we need to understand the relationship between radicals and exponents. The cube root of a number can be expressed using a rational exponent as follows:

For any number a, the cube root can be written as a^1/3. Therefore, the cube root of 2 can be written as:

2^1/3

Now, we want to find the cube root of 2⁷. We apply the exponent to the radical:

(2⁷)^1/3

When we multiply the exponents, we get:

2^7/3

Thus, the cube root of 2 to the seventh power written as a rational exponent is 2^7/3.