Questions: sqrt(81 x^14) =

Solution Steps

To solve the expression \(\sqrt{81 x^{14}}\), we need to simplify the square root of the product of a constant and a variable raised to a power. We can break it down into the square root of the constant and the square root of the variable part separately.

1. Simplify the square root of the constant 81.
2. Simplify the square root of \(x^{14}\) by using the property \(\sqrt{x^n} = x^{n/2}\).

We start with the expression \( \sqrt{81 x^{14}} \). The square root of the constant 81 can be simplified as follows: \[ \sqrt{81} = 9 \]

Next, we simplify the square root of the variable part \( x^{14} \): \[ \sqrt{x^{14}} = x^{14/2} = x^7 \]

Now, we combine the results from the previous steps: \[ \sqrt{81 x^{14}} = 9 \cdot x^7 \]

Final Answer