Answer:
[tex]h=588[/tex]
Step-by-step explanation:
Given the fraction [tex]\dfrac{4,704}{h}[/tex]
Consider its numerator and factor it:
[tex]4,704=2^5\cdot 3\cdot 7^2[/tex]
You cann not take the cube root from [tex]3, 7^2, 2^5,[/tex] you can only take the cube root from [tex]2^3[/tex], then the smallest whole number [tex]h[/tex] such that [tex]\dfrac{4,704}{h}[/tex] is a cube number is
[tex]h=2^2\cdot 3\cdot 7^2=4\cdot 3\cdot 49=588[/tex]
When [tex]h=588,[/tex]
[tex]\dfrac{4,704}{588}=8=2^3[/tex]
