Simplify `(81)^(0.16) xx (81)^(0.09)`

Answer

To simplify the expression \( (81)^{0.16} \times (81)^{0.09} \), we can follow these steps:

### Step 1: Use the property of exponents
We know that when multiplying two powers with the same base, we can add the exponents:
\[ a^m \times a^n = a^{m+n} \]
So, we can rewrite the expression as:
\[ (81)^{0.16 + 0.09} \]

### Step 2: Calculate the sum of the exponents
Now, we need to add the exponents:
\[ 0.16 + 0.09 = 0.25 \]
Thus, we can rewrite the expression as:
\[ (81)^{0.25} \]

### Step 3: Rewrite 81 as a power of 3
Next, we can express 81 in terms of a base of 3:
\[ 81 = 3^4 \]
So, we can substitute this back into our expression:
\[ (3^4)^{0.25} \]

### Step 4: Use the power of a power property
Using the property of exponents \( (a^m)^n = a^{m \cdot n} \), we can simplify further:
\[ (3^4)^{0.25} = 3^{4 \times 0.25} = 3^1 \]

### Step 5: Simplify the expression
Finally, we simplify \( 3^1 \):
\[ 3^1 = 3 \]

### Final Answer
Thus, the simplified form of \( (81)^{0.16} \times (81)^{0.09} \) is:
\[ \boxed{3} \]