Find the value of `x, " if " x^(3) = (125)/(343)`.

Options

A. 1
B. `(7)/(5)`
C. `(5)/(7)`
D. 0

Answer

To find the value of \( x \) in the equation \( x^3 = \frac{125}{343} \), we can follow these steps:

### Step 1: Factorize the numerator and denominator
We start by factorizing both the numerator (125) and the denominator (343).

- **Numerator (125)**:
- \( 125 = 5 \times 5 \times 5 = 5^3 \)

- **Denominator (343)**:
- \( 343 = 7 \times 7 \times 7 = 7^3 \)

### Step 2: Rewrite the equation
Now we can rewrite the equation using the factored forms:

\[ x^3 = \frac{125}{343} = \frac{5^3}{7^3} \]

### Step 3: Apply the property of exponents
Using the property of exponents that states \( \frac{a^n}{b^n} = \left(\frac{a}{b}\right)^n \), we can simplify the equation:

\[ x^3 = \left(\frac{5}{7}\right)^3 \]

### Step 4: Take the cube root of both sides
To solve for \( x \), we take the cube root of both sides:

\[ x = \frac{5}{7} \]

### Final Answer
Thus, the value of \( x \) is:

\[ \boxed{\frac{5}{7}} \]

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