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.
Victoria is finding the value of n for the equation
\sqrt[3]{14}\frac{1}{6}=14^{\frac{1}{n}}
1 answer