How do you rewrite the fourth root of 7 raised to the fifth power as a rational exponent?

To rewrite the expression the fourth root of 7 to the fifth power using a rational exponent, we need to understand how roots and exponents are related.

The fourth root of a number can be expressed as a rational exponent. The fourth root of a number x can be written as:

• x^1/4

Therefore, the fourth root of 7 can be written as:

• 7^1/4

Now, when we raise this expression to the fifth power, we have:

• (7^1/4)⁵

According to the rules of exponents, specifically (a^m)ⁿ = a^m*n, we can multiply the exponents:

• 7^{(1/4) * 5}

This simplifies to:

• 7^5/4

Thus, the fourth root of 7 to the fifth power can be rewritten as a rational exponent:

• 7^5/4

In summary, the fourth root of 7 raised to the fifth power is equivalent to:

• 7^5/4

This method applies the principles of exponent rules and helps clarify how roots can be expressed in exponent form.