Answer:
[tex]\frac{{5}}{w^{2}}[/tex]
Step-by-step explanation:
We begin with [tex]\frac{15w^{4}v^{5}}{3w^{6}v^{5}}[/tex].
Firstly, as with simplifying fractions we can simplify the numbers. 15 is divisible by 3, so this becomes [tex]\frac{5w^{4}v^{5}}{w^{6}v^{5}}[/tex].
To simplify indices (aka exponents or powers), we must subtract the power on the denominator from the matching one on the numerator, and then use that number as the power in the numerator. In this case, 4-6 and 5-5, which becomes -2 and 0.
So now we have [tex]\frac{5w^{-2}v^{0}}{1}[/tex].
For a negative power, we switch it into the other half (numerator to denominator) and take away the negative sign, leaving [tex]\frac{5v^{0}}{1w^{2}}[/tex].
We can remove the [tex]v^{0}[/tex] in the numerator as it just multiplies the numerator by one, and remove the 1 in the denominator for the same reason.
This leaves us with [tex]\frac{5}{w^{2}}[/tex].
**This content involves division with indices, which you may wish to revise. Let me know if you have any questions. I'm always happy to help!
