Question

value: 2
simplify
$5^{\frac{1}{5}} \cdot 5^{\frac{2}{5}}$
\\(\circ\\) a. $5^{\frac{2}{25}}$
\\(\circ\\) b. $5^{\frac{3}{5}}$
\\(\circ\\) c. $5^{\frac{1}{5}}$
\\(\circ\\) d. 3

Explanation:

Step1: Apply exponent product rule

When multiplying terms with the same base, add exponents: $a^m \cdot a^n = a^{m+n}$
$\displaystyle 5^{\frac{1}{5}} \cdot 5^{\frac{2}{5}} = 5^{\frac{1}{5} + \frac{2}{5}}$

Step2: Add the fractions

Sum the numerators over the common denominator.
$\displaystyle 5^{\frac{1+2}{5}} = 5^{\frac{3}{5}}$

Answer:

b. $5^{\frac{3}{5}}$