Final answer:
To express the positive fourth root of 5 as a fraction, we write it as 5^(1/4) which simplifies to 5.
Step-by-step explanation:
To express the positive fourth root of 5 as a fraction, we can write it as 5^(1/4). To simplify this expression, we can rewrite it as a fractional power of a fraction:
To express the positive fourth root of 5 as a fraction, we must understand the properties of exponents and roots. The fourth root of a number 'x' can be denoted as 'x' to the 1/4 power. Therefore, the fourth root of 5 can be written as 5 to the power of 1/4. Since fractions denote division, the expression 51/4 directly translates to 'the fourth root of 5'.
However, it's important to recognize that this is not a fraction in the traditional sense because 5 is not a perfect fourth power, thus it cannot be simplified to a rational number with a numerator and a denominator consisting only of integers. Instead, it remains an irrational number even though it is expressed using fractional exponents.
5^(1/4) = (5^(1/4))/(1^(1/4))
Since any number raised to the power of 1 is itself, we get:
(5^(1/4))/(1^(1/4)) = 5/1 = 5
So, the positive fourth root of 5 expressed as a fraction is 5.