Question

Please help thanks!!

Answer 1

Think kind of problems can be solved by turning roots into rational exponents. If you remember that

`\sqrt[n]{a^m} = a^{(m)/(n)}`, you have

`√(5) = 5^{(1)/(2)}, \sqrt[3]{5} = 5^{(1)/(3)}`

Moreover, recall the following rule for multiplying powers of the same base:

`a^b \cdot a^c = a^(b+c)`

to write

`√(5)\cdot \sqrt[3]{5} = 5^{(1)/(2)} \cdot 5^{(1)/(3)} = 5^{(1)/(2)+(1)/(3)}`

since
`\cfrac{1}{2}+\cfrac{1}{3} = \cfrac{5}{6}`, the result is

`5^{(5)/(6)} = \sqrt[6]{5^5}`