Question

simplify and rewrite (4x^(2)y^(-3))^(-2) using only positive exponents

Answer 1

To simplify and rewrite the expression \((4x^{2}y^{-3})^{-2}\) using only positive exponents, follow these steps:

1. Apply the power of a power property \((a^m)^n = a^{mn}\):
\[
(4x^{2}y^{-3})^{-2} = 4^{-2}(x^{2})^{-2}(y^{-3})^{-2}
\]

2. Simplify each part:
- \(4^{-2} = \frac{1}{4^2} = \frac{1}{16}\)
- \((x^{2})^{-2} = x^{-4} = \frac{1}{x^{4}}\)
- \((y^{-3})^{-2} = y^{6}\)

3. Substitute these back into the expression:
\[
\frac{1}{16} \cdot \frac{1}{x^{4}} \cdot y^{6}
\]

4. Combine the components:
\[
= \frac{y^{6}}{16x^{4}}
\]

Thus, the simplified expression with only positive exponents is:
\[
\frac{y^{6}}{16x^{4}}
\]