Victoria is finding the value of n for the equation

Question

\sqrt[3]{14}\frac{1}{6}=14^{\frac{1}{n}}

Answer 1

To find the value of n, we can simplify the equation step by step.

First, we simplify the left side of the equation:

\sqrt[3]{14} \cdot \frac{1}{6}

The cube root of 14 can be written as 14^(1/3), so the expression becomes:

14^{\frac{1}{3}} \cdot \frac{1}{6}

Next, we can rewrite the right side of the equation as:

14^{\frac{1}{n}} = (14^1)^{\frac{1}{n}} = 14^{\frac{1}{n}}

Now, our equation becomes:

14^{\frac{1}{3}} \cdot \frac{1}{6} = 14^{\frac{1}{n}}

We can set the exponents equal to each other:

\frac{1}{3} = \frac{1}{n}

To solve for n, we can take the reciprocal of both sides:

\frac{1}{\frac{1}{3}} = \frac{1}{\frac{1}{n}}

This simplifies to:

3 = n

Therefore, the value of n is 3.