Express the following as pth power of qth root of x.
`(156)^((5)/(3))`

Answer

To express \( 156^{\frac{5}{3}} \) as the pth power of the qth root of x, we can follow these steps:

### Step 1: Understand the expression
We have \( 156^{\frac{5}{3}} \). This can be interpreted as a power and a root. The denominator of the fraction indicates the root, and the numerator indicates the power.

### Step 2: Rewrite the expression
We can rewrite \( 156^{\frac{5}{3}} \) as:
\[ 156^{\frac{5}{3}} = (156^{5})^{\frac{1}{3}} \]
This means we are taking the cube root (since \( \frac{1}{3} \) is the root) of \( 156^5 \).

### Step 3: Identify p and q
In this expression:
- The pth power is \( 156^5 \)
- The qth root is the cube root, which is represented as \( \sqrt[3]{\cdot} \)

### Final Expression
Thus, we can express \( 156^{\frac{5}{3}} \) as:
\[ \sqrt[3]{156^5} \]

### Summary
So, \( 156^{\frac{5}{3}} \) can be expressed as the 5th power of the cube root of \( 156 \):
\[ \sqrt[3]{156^5} \]