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

Answer:

$5^{5/6}$

Step-by-step explanation:

we have

$\sqrt{5}\sqrt[3]{5}$

we know that

$\sqrt{5}\sqrt[3]{5}=(5^{1/2})(5^{1/3})$

Remember that

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

so

$(5^{1/2})(5^{1/3})=(5^{(1/2)+(1/3)})\\ \\=5^{5/6}$