Find x so that `(-5)^(x+1)xx(-5)^(5)=(-5)^(7)`

Answer

To solve the equation \((-5)^{(x+1)} \cdot (-5)^{5} = (-5)^{7}\), we can follow these steps:

### Step 1: Combine the powers on the left side
Using the property of exponents that states \(a^m \cdot a^n = a^{m+n}\), we can combine the left side of the equation:

\[ (-5)^{(x+1)} \cdot (-5)^{5} = (-5)^{(x+1 + 5)} = (-5)^{(x + 6)} \]

### Step 2: Set the exponents equal to each other
Since the bases are the same on both sides of the equation, we can set the exponents equal to each other:

\[ x + 6 = 7 \]

### Step 3: Solve for \(x\)
To isolate \(x\), subtract 6 from both sides:

\[ x = 7 - 6 \]

\[ x = 1 \]

### Final Answer
Thus, the value of \(x\) is \(1\).

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