Answer: See below
Step-by-step explanation:
Apply exponent rule: [tex]\left(a\cdot \:b\right)^n=a^nb^n[/tex]
[tex]\left(m^3n^5\right)^{\frac{1}{4}}=\left(m^3\right)^{\frac{1}{4}}\left(n^5\right)^{\frac{1}{4}}[/tex]
Simplify m:
[tex]\left(m^3\right)^{\frac{1}{4}}=m^{3\cdot \frac{1}{4}}[/tex]
[tex]=m^{\frac{3}{4}}[/tex]
Simplify n:
[tex]\left(n^5\right)^{\frac{1}{4}}=n^{5\cdot \frac{1}{4}}[/tex]
[tex]=n^{\frac{5}{4}}[/tex]
Final expression
[tex]=m^{\frac{3}{4}}n^{\frac{5}{4}}[/tex]
