Simplify Term 1
4^1/2
Simplify the rational exponent:
41/2
Analyze Fractional Exponent:
ab/c = (c√a)b
Take the cth root of a
Then raise that 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
Simplify Term 2
4^5/2
Simplify the rational exponent:
45/2
Analyze Fractional Exponent:
ab/c = (c√a)b
Take the cth root of a
Then raise that 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
Final Answer
45/2 = 32
