[a-2(expo.) b4(expo.)] [a2(expo.) b -5(expo.)]?

Question

When the number has (expo.) after it, that number is an exponent.

Answer 1

(a^-2 b^4)(a^2 b^-5)

= a^0 b^-1

The exponents of the "a" cancel one another.
You are left with "b" to the negative 1.
Since the b has a negative exponent, place it in the denominator:

Final answer:

1
----
b^1

or

1/b

(Use ^ to denote exponents)

Good luck in your classes.

***********************

Am I reading your question correctly?

Regards,
~ Mitch ~

Answer 2

For an exponent, use the ^ sign.

So, you have:

(a^-2 b^4)(a^2 b^-5)

Now, use the FOIL method:

First: (a^-2)(a^2) = a^0 = 1
Outer: (a^-2)(b^-5) = a^-2 b^-5
Inner: (b^4)(a^2) = a^2 b^4
Last: (b^4)(b^-5) = b^-1

So, you have:

1 + (a^-2 b^-5) + (a^2 b^4) + b^-1