Question

Express the following fraction in simplest form, only using positive exponents.
start fraction, minus, 3, left parenthesis, v, cubed, right parenthesis, to the power minus 5 , divided by, 6, s, to the power minus 7 , end fraction
6s
−7

−3(v
3
)
−5

​

Answer 1

To simplify the fraction \(-\frac{3(v^3)^{-5}}{6s^{-7}}\), we can follow these steps:

1. Rewrite the terms with negative exponents as positive exponents. Recall that \(a^{-n} = \frac{1}{a^n}\) or \(a^{-n} = \frac{1}{a^n}\).

The expression becomes:
\[
-\frac{3}{6} \cdot \frac{1}{(v^3)^5} \cdot s^7
\]

2. Simplify the expression. Start with \(-\frac{3}{6}\):
\[
-\frac{3}{6} = -\frac{1}{2}
\]

Next, simplify \((v^3)^{-5}\):
\[
(v^3)^{-5} = \frac{1}{(v^3)^5} = \frac{1}{v^{15}}
\]
Therefore, we have:
\[
-\frac{1}{2} \cdot \frac{1}{v^{15}} \cdot s^7 = -\frac{s^7}{2v^{15}}
\]

3. Thus, combining everything together, the final result is:
\[
-\frac{s^7}{2v^{15}}
\]

This is the simplest form of the given fraction with positive exponents.