Express the following in power notation.
`(-125)/( 343)`

Answer

To express \((-125)/(343\) in power notation, follow these steps:

### Step 1: Factor the Numerator and Denominator
We start by factoring both the numerator and the denominator.

- The numerator is \(-125\). We can express \(125\) as \(5 \times 5 \times 5\) or \(5^3\). Therefore, \(-125\) can be written as \(-1 \times 5^3\).

- The denominator is \(343\). We can express \(343\) as \(7 \times 7 \times 7\) or \(7^3\).

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

\[ \frac{-125}{343} = \frac{-1 \times 5^3}{7^3} \]

### Step 3: Combine the Terms
Next, we can combine the terms in the fraction:

\[ \frac{-1 \times 5^3}{7^3} = -1 \times \frac{5^3}{7^3} \]

### Step 4: Use Power Notation
We can express the fraction \(\frac{5^3}{7^3}\) using power notation:

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

### Step 5: Include the Negative Sign
Now we can include the negative sign:

\[ -1 \times \left(\frac{5}{7}\right)^3 = -\left(\frac{5}{7}\right)^3 \]

### Final Expression
Thus, the expression \(\frac{-125}{343}\) in power notation is:

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

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