If `root(5)((g-1)/(4))=(1)/(3)`, then g =

Options

A. `0.984`
B. `0.996`
C. `1.004`
D. `1.016`

Explanation

To solve the equation \( \sqrt[5]{\frac{g-1}{4}} = \frac{1}{3} \), we will follow these steps:

### Step 1: Rewrite the equation in exponential form
The expression \( \sqrt[5]{x} \) can be rewritten as \( x^{\frac{1}{5}} \). Thus, we can rewrite the given equation as:
\[ \left(\frac{g-1}{4}\right)^{\frac{1}{5}} = \frac{1}{3} \]

### Step 2: Eliminate the fifth root by raising both sides to the power of 5
To eliminate the fifth root, we raise both sides of the equation to the power of 5:
\[ \frac{g-1}{4} = \left(\frac{1}{3}\right)^5 \]

### Step 3: Calculate \( \left(\frac{1}{3}\right)^5 \)
Calculating \( \left(\frac{1}{3}\right)^5 \):
\[ \left(\frac{1}{3}\right)^5 = \frac{1^5}{3^5} = \frac{1}{243} \]
So, we have:
\[ \frac{g-1}{4} = \frac{1}{243} \]

### Step 4: Multiply both sides by 4 to isolate \( g-1 \)
Next, we multiply both sides by 4:
\[ g - 1 = 4 \cdot \frac{1}{243} \]
This simplifies to:
\[ g - 1 = \frac{4}{243} \]

### Step 5: Solve for \( g \) by adding 1 to both sides
Now, we add 1 to both sides to solve for \( g \):
\[ g = \frac{4}{243} + 1 \]

### Step 6: Write 1 as a fraction with a common denominator
To add these fractions, we convert 1 into a fraction with a denominator of 243:
\[ 1 = \frac{243}{243} \]
So, we have:
\[ g = \frac{4}{243} + \frac{243}{243} = \frac{4 + 243}{243} = \frac{247}{243} \]

### Final Answer
Thus, the value of \( g \) is:
\[ g = \frac{247}{243} \]