Simplify by writing the expression with positive exponents. Assume that all variables represent nonzero real numbers.

Question

StartFraction x Superscript negative 3 Baseline y Over 6 s Superscript negative 9 EndFraction

Answer 1

To simplify the expression \(\frac{x^{-3} y}{6 s^{-9}}\) by writing it with positive exponents, we can follow these steps:

1. Move the negative exponent terms from the numerator or the denominator:

   • The term \(x^{-3}\) can be moved from the numerator to the denominator, making it \(x^{3}\).
   • The term \(s^{-9}\) in the denominator can be moved to the numerator, becoming \(s^{9}\).

2. Rewrite the expression: \[ \frac{x^{-3}y}{6s^{-9}} = \frac{y s^{9}}{6 x^{3}} \]

3. Final expression with positive exponents: \[ \frac{y s^{9}}{6 x^{3}} \]

Thus, the simplified expression with positive exponents is: \[ \frac{y s^{9}}{6 x^{3}} \]