Simplify and express the result in exponential form :
` ((-2)/( 11))^(7) xx ((-2)/(11))^(8)`

Answer

To simplify the expression \(\left(-\frac{2}{11}\right)^{7} \times \left(-\frac{2}{11}\right)^{8}\) and express the result in exponential form, we can follow these steps:

### Step 1: Identify the Base and Exponents
The base in both terms is \(-\frac{2}{11}\) and the exponents are \(7\) and \(8\).

### Step 2: Apply the Exponent Multiplication Rule
According to the rule of exponents, when multiplying two expressions with the same base, we can add their exponents:
\[ x^a \times x^b = x^{a+b} \]
Here, we can apply this rule:
\[ \left(-\frac{2}{11}\right)^{7} \times \left(-\frac{2}{11}\right)^{8} = \left(-\frac{2}{11}\right)^{7+8} \]

### Step 3: Calculate the Sum of the Exponents
Now, we add the exponents:
\[ 7 + 8 = 15 \]

### Step 4: Write the Final Result
Now we can express the simplified result in exponential form:
\[ \left(-\frac{2}{11}\right)^{15} \]

### Final Answer
Thus, the simplified expression is:
\[ \left(-\frac{2}{11}\right)^{15} \]

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