Express each of the following in expontial notation :
` (-32)/( 243)`

Answer

To express \((-32)/(243\) in exponential notation, we can follow these steps:

### Step 1: Factor the numbers
First, we need to factor \(-32\) and \(243\) into their prime factors.

\[ -32 = -1 \times 32 = -1 \times (2 \times 2 \times 2 \times 2 \times 2) = -1 \times 2^5 \]

\[ 243 = 3 \times 3 \times 3 \times 3 \times 3 = 3^5 \]

### Step 2: Rewrite the expression
Now we can rewrite the expression \((-32)/(243)\) using the prime factorization we found:

\[ \frac{-32}{243} = \frac{-1 \times 2^5}{3^5} \]

### Step 3: Combine the terms
We can combine the terms in the expression:

\[ \frac{-1 \times 2^5}{3^5} = -1 \times \frac{2^5}{3^5} \]

### Step 4: Use the property of exponents
Using the property of exponents \(\frac{a^m}{b^m} = \left(\frac{a}{b}\right)^m\), we can simplify further:

\[ -1 \times \left(\frac{2}{3}\right)^5 \]

### Step 5: Final expression
Thus, the expression in exponential notation is:

\[ -1 \times \left(\frac{2}{3}\right)^5 \]

### Summary
The final answer in exponential notation is:

\[ -\left(\frac{2}{3}\right)^5 \]

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