Question

Find the product sqrt 5 * ^3 sqrt 5 (SEE PICTURE)

Answer 1

For this case, what you should know is that for the same base the exponents are added.
We have then:
base = 5
Exponents = (1/2) and (1/3)
Solving the product we have:
(sqrt 5) * (^ 3 sqrt 5) = 5 ^ ((1/2) + (1/3)) = 5 ^ (5/6)
answer
(sqrt 5) * (^ 3 sqrt 5) = 5 ^ (5/6)

Answer 2

`5^(5/6)`

Explanation:

we have

`√(5)\sqrt[3]{5}`

we know that

`√(5)\sqrt[3]{5}=(5^(1/2))(5^(1/3))`

Remember that

for the product of numbers with the same base the exponents are added

so

`(5^(1/2))(5^(1/3))=(5^((1/2)+(1/3)))\\ \\=5^(5/6)`