Simplify. $$ \left(\frac{2 y^{-4}}{y^{4}}\right)^{2} $$ Write your answer using only positive exponents

Question

UpStudy AI · Accepted Answer

We start with the expression:

((2 y^(-4))/(y^4))^2

Step 1: Simplify inside the parentheses. When dividing like bases, subtract the exponents:
  y^(-4) / y^4 = y^(-4 - 4) = y^(-8)

So, the expression becomes:

(2 y^(-8))^2

Step 2: Square the constant and the variable separately:
  (2 y^(-8))^2 = 2^2 * (y^(-8))^2 = 4 y^(-16)

Step 3: Rewrite with positive exponents:
  4 y^(-16) = 4 / y^(16)

Thus, the simplified expression is:

4/(y^(16))
The simplified expression is $$ \frac{4}{y^{16}} $$.

Simplify. \[ \left(\frac{2 y^{-4}}{y^{4}}\right)^{2} \] Write your answer using only positive exponents