(2a^-2)(a^6b^-1)

Question

I don't know where or how to start.

Answer 1

you are multiplying the two expressions, it can be written as (2a^-2)(a^6b^-1) 2a^-2

                                                                                                                    a^6b^-1

 

This might help

 

The statement A ∧ B is true if A and B are both true; else it is false.
 
exponentiation
… (raised) to the power of …
everywhere
a ^ b means a raised to the power of b

(a ^ b is more commonly written ab. The symbol ^ is generally used in programming languages where ease of typing and use of plain ASCII text is preferred.)

Answer 2

Well, Raven, let's see where your problem lies. Do you know what the expressions mean = how to write them longhand? That would be (as spoken text, reading what you should write): 

open parenthesis two a to the minus 2 power close parenthesis

times

open parenthesis a to the 6th power, times b to the minus one power close parenthesis

 

Another word for "power" is "exponent"; maybe your class uses that instead?

 

Is that good so far? I'll assume you know what powers are : positive powers mean you multiply the variable in question (called the "argument") -- here variously "a" or "b" -- by itself that many times; negative powers mean you divide by that variable that many times.

 

So, the next thing to consider is, what of these items can be put together (simplified = consolidated)?

-- any constants can always be multiplied

-- any of the same variable can be put together. The rule for "putting together" when dealing with powers of a variable, is, to MULTIPLY the terms (which is what you're doing with the central "times"), you ADD the powers on that variable.

 

So for "a" adding the powers: negative 2 plus positive 6 = positive 4

for "b" you only have what you started with: power of negative one.

For the constants, there's only one: the "2" in from of the first "a"

SO putting it all together, in the order you should calculate and write it:

Answer = two a to the positive 4 power b to the negative 1 power,

which you would type as 2a^4b^-1,

and which means "two times (a * a * a * a)/b"

OK?