4^1/2*4^5/2

<-- Enter Number or variable Raised to a fractional power such as a^b/c

Term 1
Simplify the rational exponent 41/2

Analyze Fractional Exponent:
The rule of fractional exponents states that ab/c is evaluated as follows:
ab/c = (ca)b
That is equivalent to saying we take the cth root of a, and then raise that value to the power of b
In this case, a = 4, b = 1, and c = 2

Evaluate the 2 root of 4:
4 = 2 since 22 = 4
Raise this value to the power of 1:
Therefore, we can write 41/2 = 2

Term 2
Simplify the rational exponent 45/2

Analyze Fractional Exponent:
The rule of fractional exponents states that ab/c is evaluated as follows:
ab/c = (ca)b
That is equivalent to saying we take the cth root of a, and then raise that value to the power of b
In this case, a = 4, b = 5, and c = 2

Evaluate the 2 root of 4:
4 = 2 since 22 = 4
Raise this value to the power of 5:
Therefore, we can write 45/2 = 32

Finalize our product of rational exponents:
41/2 x 45/2 = 2 x 32
41/2 x 45/2 = 64