Simplify the expression start fraction 10 r superscript negative 2 baseline over r squared w superscript negative 3 baseline end fraction.

Question

(1 point)
Responses

10 w cubed
Image with alt text: 10 w cubed

start fraction r superscript 4 baseline over 100 w cubed end fraction
Image with alt text: start fraction r superscript 4 baseline over 100 w cubed end fraction

start fraction w cubed over 100 r superscript 4 baseline end fraction
Image with alt text: start fraction w cubed over 100 r superscript 4 baseline end fraction

start fraction 10 w cubed over r superscript 4 baseline end fraction

Answer 1

To simplify the expression \(\frac{10 r^{-2}}{r^2 w^{-3}}\), we can follow these steps:

1. Rewrite the expression by removing the negative exponents: \[ \frac{10}{r^2} \cdot \frac{w^3}{1} = \frac{10 w^3}{r^2} \]

2. Since the denominator has \(r^2\) which is \(r^{2}\) and the numerator has \(r^{-2}\), combine the powers of \(r\): \[ \frac{10 w^3}{r^2} = \frac{10}{r^{2-(-2)}} w^3 = \frac{10 w^3}{r^4} \]

Now, we end up with: \[ \frac{10 w^3}{r^4} \]

Thus, the simplified expression is: \[ \frac{10 w^3}{r^4} \]

The correct response is: start fraction 10 w cubed over r superscript 4 baseline end fraction.