SOLUTION: Can ANYONE help me with ANY of these? 1) Use the rules of exponents to evaluate or simplify. Write without negative exponents. 3*4^0 = ____ 2) Use the rules of expo

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Let's review the rules of exponents. In these rules, the "variables" stand for any expression (unless there is a note to the contrary). They are numbered so they can be referred to by number, not because any of them are more important or useful than another.)

1. A power of a power:
2. Multiplication with the same base: (Pay close attention to the difference between this rule and rule #1!)
3. Division with the same base:
4. Negative exponents: or . In words, stands for the reciprocal of a^n.
5. Zero exponents: Note: a must not be zero!
6. Fractional exponents (where "n" and "m" are positive integers):
   • . So , , , etc.}}}
   • Using the above rule and rule #1 together:
7. The pseudo-distributive property. This property is not the distributive property but it does look a little like the distributive property:
8. Exponents apply only to what is immediately in front of them! If the symbol immediately in front of an exponent is a grouping symbol, then the exponent is applied to the entire expression in the grouping symbol. Examples:
   • 
   • 
   • . Note the difference between this example and the previous one. Here a ")" is right in front of the exponent. So the exponent applies to everything in the parentheses. In the previous example, a "4" is right in front of the exponent. So the exponent applies only to the 4 (and not the "-"!)
   • 
   • 

Now let's try to solve your problems.
1) Use the rules of exponents to evaluate or simplify. Write without negative exponents.
3*4^0 = ____
According to PEMDAS (the order of operations) we need to simplify the exponent before doing the multiplication. So we need to figure out 4^0 first. Using rule #5 we find that 4^0 = 1. Substituting this in we get
3*1 = ____
which, of course, is 3.

2) Use the rules of exponents to evaluate or simplify. Write without negative exponents.
1 / 4^-2 = ____
Using the 2nd variation of rule #4:


3) Use the rules of exponents to evaluate or simplify. Write without negative exponents.
(1/4)^-1/2 = _____
Using rule #1, in "reverse", we can rewrite this as:

Then, using rule #4, the expression in the parentheses can be simplified: . Substituting we get:
which, according to rule #6, is

4) Use the rules of exponents to evaluate or simplify. Write without negative exponents.
(bm)^-3 = ____
Using rule #1 again we can rewrite this as:

Using rule 7:

Using rule #4:


5) Use the rules of exponents to evaluate or simplify. Write without negative exponents.
y^-5 / y^-2 = ____
Using rule #3

Using rule #4 we get


6) Use the rules of exponents to evaluate or simplify. Write without negative exponents.
(-243)^3/5 = ____
Using the second variation of rule #6:

Since . Substituting into the above we get


7) Use the rules of exponents to evaluate or simplify. Write without negative exponents.
36^1/2 = ____
Using rule #6