1. The 5/65 can be simplified, the a³ moves to the denominator, and bc is canceled from the numerator and denominator.
[tex] \frac{5a^3 bc^2}{65 a^4 bc} = \frac{c}{13a} [/tex]
2. The 10/125 can be simplified, the a³ moves to the denominator, and bc is canceled from the numerator and denominator.
[tex] \frac{10a^3bc^2}{125a^4bc} = \frac{2c}{25a} [/tex]
3. The 65/5 simplifies, the a³ moves to the numerator, and bc is canceled from the numerator and denominator.
[tex] \frac{65a^4 bc^2}{5a^3 bc} = 13ac [/tex]
4. The 10/130 simplifies, the b² cancels out in the numerator and denominator, and the [tex]c^4[/tex] moves to the numerator.
[tex] \frac{10b^2 c^5}{130a^4b^2c^4} = \frac{c}{13a^4}[/tex]
5. The 10/130 simplifies, the b² cancels out in the numerator and denominator, the [tex]a^4[/tex] moves to the numerator, and the [tex]c^4[/tex] moves to the numerator.
[tex] \frac{10a^5b^2c^5}{130a^4b^2c^4} = \frac{ac}{13} [/tex]
I believe the only expression that simplifies to [tex] \frac{c}{13a}[/tex] is the first one.
