%5E(0.16)times(256)%5E(0.09)%3D.jpeg "(256)^(0.16)times(256)^(0.09)=")
Evaluation of Exponential Expression
In this article, we will evaluate the exponential expression (256)^(0.16) × (256)^(0.09).
Breaking Down the Expression
To start, let's break down the expression into smaller parts:
(256)^(0.16): This is a power expression where 256 is raised to the power of 0.16.(256)^(0.09): This is another power expression where 256 is raised to the power of 0.09.×: This is the multiplication operator, which means we need to multiply the results of the two power expressions.
Evaluating the Power Expressions
To evaluate the power expressions, we need to use the property of exponentiation, which states that a^(m) × a^(n) = a^(m+n).
First Power Expression: (256)^(0.16)
To evaluate (256)^(0.16), we can use the fact that 256 is equal to 2^8. Therefore:
(256)^(0.16) = (2^8)^(0.16) = 2^(8×0.16) = 2^1.28
Second Power Expression: (256)^(0.09)
To evaluate (256)^(0.09), we can use the same approach as before:
(256)^(0.09) = (2^8)^(0.09) = 2^(8×0.09) = 2^0.72
Multiplying the Results
Now that we have evaluated both power expressions, we can multiply the results:
(2^1.28) × (2^0.72) = 2^(1.28+0.72) = 2^2
Final Answer
Therefore, the final answer is:
(256)^(0.16) × (256)^(0.09) = 2^2 = 4
And that's the result of evaluating the exponential expression `(256)^(0.16) × (256)^(0.09)!
