Answer:
Your friend made a mistake when multiplying the coefficients of each term and when adding the exponents of each term.
Correct answer: [tex]\left(12a\right)^{7/10}[/tex]
Step-by-step explanation:
We can use the exponent property [tex]a^b\cdot a^c=a^{(b+c)}[/tex] to solve this problem.
Substituting given values, we get:
[tex]4a^{(\frac{1}{2})}\cdot 3a^{(\frac{1}{5})}=12a^{(\frac{1}{2}+\frac{1}{5})}=12a^{(\frac{5}{10}+\frac{2}{10})}=\boxed{12a^{(\frac{7}{10})}}[/tex]
