simplify : `\left(4x^{3}y^{-4}\right)^{-2}`.

1 answer

To simplify the expression (4x3y4)2, we will apply the property of exponents (am)n=amn.

Starting with the expression:

(4x3y4)2

we can distribute the exponent 2 to each term inside the parentheses:

=42(x3)2(y4)2

Now, let's simplify each part:

  1. 42=142=116
  2. (x3)2=x6
  3. (y4)2=y8

Putting this all together, we get:

=116x6y8

Now, we can express x6 as 1x6:

=y816x6

Thus, the simplified form of the expression (4x3y4)2 is:

y816x6