The LCM of `27a^(5) and 81a^(10)` is `3^(4)a^(10)`. If the given statement true?

Answer

To determine if the statement that the LCM of \(27a^5\) and \(81a^{10}\) is \(3^4a^{10}\) is true, we will calculate the LCM step by step.

### Step 1: Factor the coefficients
First, we factor the coefficients of the two terms:
- \(27 = 3^3\)
- \(81 = 3^4\)

So we can rewrite the terms as:
- \(27a^5 = 3^3a^5\)
- \(81a^{10} = 3^4a^{10}\)

### Step 2: Identify the highest power of each factor
Next, we find the LCM by taking the highest power of each factor present in the terms:
- For the base \(3\), the highest power between \(3^3\) and \(3^4\) is \(3^4\).
- For the base \(a\), the highest power between \(a^5\) and \(a^{10}\) is \(a^{10}\).

### Step 3: Write the LCM
Now, we can write the LCM:
\[ \text{LCM} = 3^4a^{10} \]

### Step 4: Compare with the given statement
The given statement claims that the LCM is \(3^4a^{10}\). Since we have calculated the LCM to be \(3^4a^{10}\), we can conclude that the statement is indeed true.

### Final Answer
Thus, the given statement is true.

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