Answer: The correct answer is: [C]: " [tex]15^{(7/4)}[/tex] " .
____________________________________
Step-by-step explanation:
____________________________________
Note the property for square roots in exponential form:
_____________________________________
→ [tex]\sqrt[a]{(b)^ c}[/tex] ; ↔ b[tex]b^{(c/a)}[/tex] ;
{ [tex]a\neq 0[/tex] ; [tex][a^{(b/c)}]\neq 0[/tex] ; [tex]c\neq 0[/tex] .}.
_____________________________________
As such, given:
→ [tex]\sqrt[4]{(15^7)}[/tex] ;
a = 15, b = 7, c = 4 .
→ [tex]\sqrt[4]{(15^7)}[/tex] ; ↔ [tex]15^{(7/4)}[/tex] ;
→ which corresponds to:
_____________________________________
Answer choice: [C]: " [tex]15^{(7/4)}[/tex] " .
_____________________________________
Hope this helps!
Wishing you well in your academic endeavors!
_____________________________________
