Final answer:
a) Simplify 2^3 * 2^(-2) as 2. b) Evaluate e^(ln(5)) as 5. c) Simplify (3^2)^(-1) as 1/9. d) Find the value of 4^(1/2) as 2.
Step-by-step explanation:
a) Simplify 2^3 * 2^(-2):
When multiplying powers with the same base, you add the exponents. Therefore, 2^3 * 2^(-2) can be simplified as 2^(3+(-2)) = 2^1 = 2.
b) Evaluate e^(ln(5)):
The natural logarithm (ln) and exponential function (e^x) are inverse functions, so e^(ln(5)) simplifies to just 5.
c) Simplify (3^2)^(-1):
When raising a power to a negative exponent, you can flip the base and change the exponent to positive. Therefore, (3^2)^(-1) can be simplified as 1/(3^2) = 1/9.
d) Find the value of 4^(1/2):
Raising a number to the power of 1/2 is the same as finding the square root of that number. Therefore, 4^(1/2) = √4 = 2.