Question

Use the product of powers property to simplify the numeric expression.

Answer 1

Answer:

The value of $4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}$  is  $4^{\dfrac{8}{15}}$ .

Step-by-step explanation:

We need to simplify the numeric expression using property. The expression is as follows :

$4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}$

The property to be used is : $x^a{\cdot} x^b=x^{a+b}$

This property is valid if the base is same. Here, base is x.

In this given problem, x = 4, a = 1/3 and b = 1/5

So,

$4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}}=4^{\dfrac{1}{3}+\dfrac{1}{5}}\\\\=4^{\dfrac{5+3}{15}}\\\\=4^{\dfrac{8}{15}}$

So, the value of $4^{\dfrac{1}{3}} {\cdot} 4^{\dfrac{1}{5}$  is  $4^{\dfrac{8}{15}}$ .