The given functions are: f(x)=x2+10x f(x) = x^{2} + 10x f(x)=x2+10x g(x)=5x g(x) = \frac{5}{x} g(x)=x5
To find f(x)⋅g(x) f(x) \cdot g(x) f(x)⋅g(x), multiply the expressions for f(x) f(x) f(x) and g(x) g(x) g(x): f(x)⋅g(x)=(x2+10x)⋅(5x) f(x) \cdot g(x) = (x^{2} + 10x) \cdot \left( \frac{5}{x} \right) f(x)⋅g(x)=(x2+10x)⋅(x5)
Distribute 5x \frac{5}{x} x5 to each term in x2+10x x^{2} + 10x x2+10x: f(x)⋅g(x)=x2⋅5x+10x⋅5x f(x) \cdot g(x) = x^{2} \cdot \frac{5}{x} + 10x \cdot \frac{5}{x} f(x)⋅g(x)=x2⋅x5+10x⋅x5 Simplify each term: f(x)⋅g(x)=5x+50 f(x) \cdot g(x) = 5x + 50 f(x)⋅g(x)=5x+50
5x+50\boxed{5x + 50}5x+50
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