Question

Write 312m as an expression with a rational exponent.
312m^1/6
(312m)^1/6
312^1/6m
(312m)^6

Answer 1

To express \( 312m \) with a rational exponent, we want to write it in the form of \( (a \cdot b)^c \). The options you provided seem to suggest different ways to express this.

The two expressions you listed that maintain the integrity of both parts (the number and the variable) in a single rational exponent are:

1. \( (312m)^{1/6} \)
2. \( 312^{1/6}m^{1/6} \)

However, if we are strictly looking for a single expression with a rational exponent, the most appropriate form would be:

**Option 2:** **\( (312m)^{1/6} \)**

This indicates that both \( 312 \) and \( m \) are raised to the power of \( \frac{1}{6} \).

So, it's best to choose **\( (312m)^{1/6} \)** as the answer.