Question

$4 ^{ \frac{1}{3} } \times 4 ^{ \frac{1}{5} } =$pls answer this

Answer 1

The given Expression is :

$4^{\frac{1}{3}}\cdot4^{\frac{1}{5}}$

From the property of exponents

If the base value of the exponents are same then during the process of multiplication powers will add up.

Since in the given expression 4 is the base value on both base of the exponents

Thus, base value are equal

The powers will add up:

$\begin{gathered} 4^{\frac{1}{3}}\cdot4^{\frac{1}{5}} \\ 4^{\frac{1}{3}+\frac{1}{5}} \end{gathered}$

Simplify the farction of the exponents :

$\begin{gathered} \frac{1}{3}+\frac{1}{5} \\ \text{Taking LCM of the 3 \& 5} \\ \frac{1}{3}+\frac{1}{5}=\frac{5+3}{15} \\ \frac{1}{3}+\frac{1}{5}=\frac{8}{15} \end{gathered}$

So, the value of the given expression will be :

$\begin{gathered} 4^{\frac{1}{3}}\cdot4^{\frac{1}{5}}=4^{\frac{1}{3}+\frac{1}{5}} \\ 4^{\frac{1}{3}}\cdot4^{\frac{1}{5}}=4^{\frac{8}{15}} \end{gathered}$

Answer : 4 ^8/15