`(xy)^(n)=x^(n)xx` _______.

Answer

To solve the equation \((xy)^{n} = x^{n} \cdot \_\_\_\_\_\_\_\_\), we will use the properties of indices. Here’s a step-by-step solution:

### Step 1: Understand the left side of the equation
The expression \((xy)^{n}\) means that we are raising the product of \(x\) and \(y\) to the power of \(n\).

**Hint:** Remember the property of indices that states \((a \cdot b)^{m} = a^{m} \cdot b^{m}\).

### Step 2: Apply the property of indices
Using the property mentioned, we can rewrite \((xy)^{n}\) as:
\[ (xy)^{n} = x^{n} \cdot y^{n} \]

**Hint:** This property allows you to distribute the exponent \(n\) to both \(x\) and \(y\).

### Step 3: Substitute back into the equation
Now we can substitute this result back into our original equation:
\[ x^{n} \cdot y^{n} = x^{n} \cdot \_\_\_\_\_\_\_\_\ \]

**Hint:** We are looking for what \(y^{n}\) should be in the blank.

### Step 4: Identify the blank
From our equation, we see that \(y^{n}\) must fill in the blank. Thus, we have:
\[ (xy)^{n} = x^{n} \cdot y^{n} \]

So, the complete equation is:
\[ (xy)^{n} = x^{n} \cdot y^{n} \]

### Final Answer
The blank can be filled with \(y^{n}\). Therefore, the complete equation is:
\[ (xy)^{n} = x^{n} \cdot y^{n} \]

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