Rewrite the Radical as a Rational Exponent: The Fourth Root of 7 to the Fifth Power

To rewrite the expression The Fourth Root of 7 to the Fifth Power, we can break it down step-by-step. The fourth root of any number can be expressed using a rational exponent as follows:

If we take the fourth root of a number, say x, we can write it as:

x^1/4

In this situation, we’re dealing with the number 7, so the fourth root of 7 is:

7^1/4

Now, when this is raised to the fifth power, we can express it as:

(7^1/4)⁵

According to the laws of exponents, when we raise a power to a power, we multiply the exponents:

7^{(1/4) * 5}

Calculating this gives us:

7^5/4

So, The Fourth Root of 7 to the Fifth Power rewritten as a rational exponent is:

7^5/4