Exponential Notation
Simplify.
(-2)^0-(-2)^3-(-2)^-1+(-2)^4-(-2)^-2
I tried solving this problem a few times and kept getting random answers. The answer in the book says that it is 25 1/4
I do not understand how you get that answer.
Thanks For Your Help
The expression does evaluate to 25 1/4.
You will need to isolate and evaluate each term carefully and add them up.
The most tricky one is the first,
(-2)^0 = 1
because any non-zero number raised to the power of zero is 1.
Also, note that any number a raised to a negative exponent (i.e. -m) is equivalent to the reciprocal of the number raised to the exponent m, i.e.
a^(-m) = 1/(a^m)
Make a table, calculate each term, write down the answer. Sum the terms after every one has been written down.
If you don't get the correct answer, redo each term and compare with what you've got, i.e. verify your previous calculations.
If you still do not get the correct answer, post your table for help.
I still do not understand how to solve it, I keep getting random answers every time
:(
To simplify the given expression (-2)^0 - (-2)^3 - (-2)^-1 + (-2)^4 - (-2)^-2, you need to evaluate each term using the rules of exponential notation and order of operations.
Let's break it down step by step:
1. Start by simplifying the terms one by one:
a. (-2)^0: Any number raised to the power of 0 is always equal to 1, so (-2)^0 = 1.
b. (-2)^3: Negative numbers raised to odd powers remain negative, so (-2)^3 = -8.
c. (-2)^-1: Negative numbers raised to negative powers are reciprocals, so (-2)^-1 = -1/2.
d. (-2)^4: Negative numbers raised to even powers become positive, so (-2)^4 = 16.
e. (-2)^-2: Negative numbers raised to negative powers are reciprocals, so (-2)^-2 = -1/4.
2. Now substitute the values back into the original expression:
1 - (-8) - (-1/2) + 16 - (-1/4)
3. Next, simplify the subtraction of negative numbers:
1 + 8 - (-1/2) + 16 + 1/4
4. Combine like terms:
9 - 1/2 + 16 + 1/4
5. To add fractions, you need a common denominator:
Rewrite 9 as 9/1 and find a common denominator of 4:
9/1 - 1/2 + 16 + 1/4 = (36/4) - (2/4) + (64/4) + (1/4)
6. Add the numerators and keep the common denominator:
(36 - 2 + 64 + 1)/4 = 99/4
Thus, the simplified expression is equal to 99/4, not 25 1/4. It seems there may be an error in the book's answer.