Exponential Notation
Evaluate the following:
x^-4 for x=2
I understand the -(2x2x2x2) equals 16 but the answer in the book says 1/16
How do you get 1/16?
recall some laws of exponents. a term which is raised by a negative number is also equal to its reciprocal raised to that number with positive sign. for example,
3^(-2) = (1/3)^2
thus, we can rewrite it as,
(1/x)^4
substituting x = 2,
(1/2)^4
(1/2)*(1/2)*(1/2)*(1/2)
1/16
hope this helps~ :)
Thanks so much :))
To evaluate the expression x^-4 for x=2, we need to understand exponential notation. In exponential notation, any number raised to a negative power can be rewritten as the reciprocal of the number raised to the positive power.
In this case, x^-4 can be rewritten as 1/x^4. Plugging in x=2 into this expression, we get 1/2^4, which simplifies to 1/16.
To understand why 1/16 is the correct answer, let's break it down step by step:
1. Start with x^-4.
2. Rewrite it as 1/x^4. (This is the rule for negative exponents.)
3. Substitute x=2, which gives us 1/2^4.
4. Simplify 2^4, which is 2 x 2 x 2 x 2 = 16.
5. So, the final result is 1/16.
In conclusion, when evaluating x^-4 with x=2, it simplifies to 1/16 by following the rules of negative exponents and simplifying the expression.