Using the properties of exponents, which expression is equivalent to x/3/4x?

1 answer

To simplify the expression \( \frac{x}{3} \div 4x \), we can rewrite the division as multiplication by the reciprocal:

\[ \frac{x}{3} \div 4x = \frac{x}{3} \times \frac{1}{4x} \]

Now, we multiply the fractions:

\[ \frac{x \cdot 1}{3 \cdot 4x} = \frac{x}{12x} \]

Next, we can simplify \( \frac{x}{12x} \). Since \( x \) is in both the numerator and the denominator, we can cancel it out (assuming \( x \neq 0 \)):

\[ \frac{x}{12x} = \frac{1}{12} \]

Thus, the expression \( \frac{x}{3} \div 4x \) simplifies to:

\[ \frac{1}{12} \]

So, the final equivalent expression is:

\[ \frac{1}{12} \]