Question

fully simpifly
(x^-9*x^4)^3/(x^2*x^3)^2

Answer 1

To simplify the expression \((x^{-9} \cdot x^4)^3 / (x^2 \cdot x^3)^2\), we'll use the properties of exponents.

1. **Simplify the numerator:**
\[
(x^{-9} \cdot x^4)^3 = x^{(-9 + 4) \cdot 3} = x^{-5 \cdot 3} = x^{-15}
\]

2. **Simplify the denominator:**
\[
(x^2 \cdot x^3)^2 = x^{(2 + 3) \cdot 2} = x^{5 \cdot 2} = x^{10}
\]

3. **Putting it together:**
\[
\frac{x^{-15}}{x^{10}} = x^{-15 - 10} = x^{-25}
\]

4. **Express in positive exponent form:**
\[
x^{-25} = \frac{1}{x^{25}}
\]

Thus, the fully simplified expression is:
\[
\frac{1}{x^{25}}
\]