Step-by-step explanation:
any root of a number can be written as fraction in the exponent of that number.
so, here, the square root of 5 is 5^1/2.
and the cubic root of 5 is 5^1/3.
what happens, when we multiply the same base number with exponents ?
a^n × a^m = a^(n+m)
and so we get here
5^1/2 × 5^1/3 = 5^(1/2 + 1/3)
how do we add fractions with different denominators ?
we bring them to the same denominator, usually by using the smallest (or least) common multiple of the existing denominators, which is 6 for 2 and 3.
so,
1/2 + 1/3 = 3/6 + 2/6 = 5/6
therefore, the simplified solution is
5^5/6
the first answer option is correct.
