Question

(a + b) to the power of -1 multiplied with (a + b) to the power of -1. What's the answer?

Answer 1

according to concept of surd,
if x^m and x^n multiply with each other then ,
x^m.x^n=x^(m+n)
now use this ,
( a + b)^(-1). ( a + b )^(-1)=( a + b )^(-1-1)
=( a + b )^-2

Answer 2

Data:
$(a+b)^{-1}*(a+b)^{-1} = ?$

Solving:
$(a+b)^{-1}*(a+b)^{-1} =$
Potentiation rule: Given any number, raised to the negative power {-1}, its inverse is the fraction whose numerator is 1, and the denominator is any number.
$\frac{1}{(a+b)} * \frac{1}{(a+b)} =$
Now multiply
$\frac{1}{(a+b)^2} =$ or $(a+b)^{-1+(-1)} = (a+b)^{-2}$
In the denominator we have a square of the sum of two terms. All this expression, when reduced, forms the remarkable product, which is given by: (The square of the sum of two terms is equal to the square of the first term, plus twice the first term by the second, plus the square of the second term).
$\frac{1}{(a+b)^2} =$
$\frac{1}{a^2+2*a*b+b^2} =$
[tex]\boxed{\frac{1}{a^2+2ab+b^2}} or \boxed{(a+b)^{-2}} [/tex]